alg 2 sem 1 printout checkups

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1.1.2 Checkup: Practice Problems Checkup

Algebra I Sem 2 (S3124823) Name: ____________________ Date: ____________

Answer the following questions using what you've learned from this lesson. Write your responses in thespace provided.

For questions 1 – 2, draw or describe the next picture in the pattern.

1. 2.

For questions 3 – 6, find the next part of the pattern of letters.

3. ab, de, gh, ___ 4. em, gn, io, kp, ___ 5. h, k, n, q, ___ 6. c, a, y, w, ___

For questions 7 – 10, find the next number in the pattern.

7. 8. 9. 10.

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For questions 1 – 2, find the common difference between the terms of the arithmetic sequence.

1. 2.

For questions 3 – 8, write the simple formula for the nth term of the arithmetic sequence.

3. 4. 5.

6. 7. 8.

For questions 9 – 10, given the explicit formula for an arithmetic sequence, write the recursive formula in theform .

9. 10.






For questions 1 – 2, find the common ratio of the geometric sequence.

1. 2.

For questions 3 – 5, find the first term of the geometric sequence.

3. 4. 5.

For questions 6 – 10, write the explicit formula for the geometric sequence.

6. 7. 8.

9. 10.






For questions 1 – 4, classify the sequence as arithmetic, geometric, Fibonacci, or pyramidal.

1. 10, 12.1, 14.2,16.3, ...

2. 1, 5, 14, 30, ... 3. 1, 1, 2, 3, ... 4. 7, 10.5, 15.75,23.625 ...

For questions 5 – 6, solve the problem about arithmetic sequences.

5. $650 is invested in an account at 3% simpleinterest per quarter. Write the first 5 terms ofthe sequence that shows the value of theaccount at quarterly intervals.

6. Write the next term in the constant velocitysequence.

For questions 7 – 8, solve the problem about geometric sequences.

7. You invest $2500 at an interest rate that iscompounded annually. After 8 years, yourprincipal has increased to $3292.02. What isthe interest rate?

8. Jeannie owes $750 on her credit card. Thecredit card company charges 1.5% compoundinterest per month on the balance. Write thefirst 4 terms of the sequence that wouldrepresent her balance each month if she wereto make no payments.



For questions 9 – 10, solve the problem about the pyramidal sequence.

9. In the pyramidal sequence, what number isadded to the 7th term to get the 8th term?

10. Using the pyramidal sequence, how manycannonballs are there in the bottom layer of astack of cannonballs that has 13 layers?






1.5.1 Checkup: Sequences and Functions PracticeProblems

Checkup



For questions 1 – 2, find the next part of the pattern.

1. ao, cn, em, gl, ___ 2. 1, 6, 36, 216, ___

For questions 3 – 5, determine whether the sequence is arithmetic, geometric, or neither.

3. 2, 4, 6, 12, 24 4. 5. 24, 12, 6, 3,

For questions 6 – 8, answer the questions about arithmetic sequences.

6. What is the missing term inthe arithmetic sequencebelow?

17, ___, 35, ...

7. Use the explicit formula to find

the 150th term of thesequence below.

19, 25, 31, 37, 43, ...

8. Use the explicit formula to find

the 400th term of thesequence below.

8, 20, 32, 44, 56, ...

For questions 9 – 11, write the explicit formula for the geometric sequence.



9. A geometric sequence isdefined recursively by

. The 1st term ofthe sequence is 2.7. Writethe explicit formula for thesequence.

10. 2, 8, 32, 128, ... 11. 0.5, 0.1, 0.02, 0.004, ...

For questions 12 – 14, answer the questions about geometric sequences.

12. What is the 9th term of thegeometric sequence below?



8000, 4000, 2000, 1000, ...









For question 1, determine which of the following are examples of numerical data sets.

1. Of the following, which are examples of numerical data sets? Choose all that apply:

Answer Choices:Number of black jelly beans in each jar.Heights of all of the high school basketball players.Favorite colors of all of the freshmen.Time it takes for each student to stand in line during lunch.

For question 2, determine which of the following are examples of categorical data sets.

2. Of the following, which are examples of categorical data sets? Choose all that apply:

Answer Choices:Favorite ice cream flavors.Points scored by the Lakers during the month of January.Types of pets owned.College each senior is planning to attend.

For question 3, determine which of the following are examples of discrete data sets.

3. Of the following, which are examples of discrete data sets? Choose all that apply:

Answer Choices:Number of errors committed each season by Alex Rodriguez.Number of songs on each of your friends' iPods.Amount of money you spend each week.The distance each student can run in 12 minutes.



For question 4, determine which of the following are examples of continuous data sets.

4. Of the following, which are examples of continuous data sets? Choose all that apply:

Answer Choices:Number of siblings each student in your school has.Distance, in miles, each student lives from school.Height, in inches, of each student in your history class. Time it takes, in seconds, for each student to run 100 meters.

For questions 5 – 6, use the following stemandleaf plot to answer the questions.

5. How many students took the Chapter 9 test inMs. Smith's Algebra Class?

Answer Choices:99.26.31. There is not enough information given toanswer this question.

6. What is the difference between the highestscore and the lowest score on the Chapter 9test?

Answer Choices:7.52.47. 151.

For questions 7 – 8, use the following frequency distribution to answer the questions.

Phone Count

iPhone 146

Droid X 123

Thunderbolt 84

Atrix 4G 47

7. How many students were surveyed?

Answer Choices:

8. What percent of those surveyed own aThunderbolt?Answer Choices:



146.500.99. 400.

21%.84%.400%.18%.

For questions 9 – 10, use the following bar graph to answer the questions.

9. How many students were surveyed?


10. How many more students named the Yankeesas their favorite baseball team, when comparedwith the Blue Jays?










For questions 1 – 3, use the following data set to calculate the mean, median, and mode.

Jamie McAllister is a wonderful rebounder for her high school basketball team. Of her final 10 games, here areher rebound totals for each game:

8 12 8 11 15 6 9 8 10 8

1. From the collected data,what is the mean reboundsJamie had per game?

Answer Choices:8.9.5.8.5.10.

2. From the collected data,what is the mode ofrebounds Jamie had for herfinal 10 games?


3. From the collected data,what is the medianrebounds Jamie had for herfinal 10 games?



Michelle's parents were trying to get an idea of her cell phone habits. Of Michelle's last 10 phone calls, here arethe lengths of her calls in minutes:

4. From the collected sampledata, what is the mode?


5. From the collected sampledata, what is the mean ofminutes per call?


6. From the collected sampledata, what is the median ofminutes per call?




For questions 7 – 8, you will be given all the numbers of a data set except one. Use this information to answerquestions about median, mode, and mean.

A data set is composed of the following numbers:

1, 4, 6, 6, 10, nThe mode = 6The median = 6The mean > 10

7. What is a possible value for n?

Answer Choices:6.10.100.Cannot determine with given information.

8. What must n equal in order to have a meanof 5?

Answer Choices:30.5.3.6.

For question 9, use the given word problem to answer the question.

9. Johnny has an average of an 88% on all of his algebra exams. (Each exam is worth 100 points.) He hastaken 5 exams. He wants to average a 90% and he has 1 exam left. What must he score on his last exam toaverage a 90% on all 6 exams?

Answer Choices:88%.90%.92%.100%.

For question 10, find the student's GPA.

10. Veronica is taking three AP classes and two regular classes. Her AP classes count twice as much as herregular classes in her GPA. Each A is worth 4 points, Bs are worth 3 points, Cs are worth 2 points, and Ds areworth 1 point. What is Veronica's GPA?

Answer Choices:



2.82.93.03.8









For questions 1 – 4, use the following data set to calculate the mean, range, variance, and standard deviation.

A company decides to investigate the number of sick days its employees take during the year. A sample of 6employees gave the following data for the past year:

0 4 0 2 6 0

1. From the collecteddata, what is therange of sick daystaken during thepast year from thissample?


2. From the collecteddata, what is theaverage number ofsick days takenduring the pastyear from thissample?


3. From the collecteddata, what is thevariance of sickdays taken duringthe past year fromthis sample?

Answer Choices:6.6.33.6.4. 32.

4. From the collecteddata, what is thestandard deviationof sick days takenduring the pastyear from thissample?



Mr. Lewis asked his students the following question:"How many children do you think make up the ideal family?"A sample of 7 of his students answered the question with these responses:

0 2 0 2 1 0 2

5. From the collectedsample data, whatis the range oftheir replies?

Answer Choices:2.

6. From the collectedsample data, whatis the average oftheir replies?

Answer Choices:2.

7. From the collectedsample data, whatis the variance oftheir replies?

Answer Choices:2.

8. From the collectedsample data, whatis the standarddeviation of theirreplies?

Answer Choices:



1.0.3.

1.0.3.

1.0.3.

2.1.0.3.

For questions 9 – 10, you will be given information summarizing a sample data set. Then a mathematicaloperation will be conducted on all of the data points within the data set. Answer the following questions aboutthe summary statistics after the mathematical operations have been conducted.

9. A data set had a mean of 5 and a standarddeviation of 2. Each number within this dataset is multiplied by 3. What is the new meanand standard deviation?

Answer Choices:mean = 5 standard deviation = 2.mean = 15 standard deviation = 2.mean = 5 standard deviation = 6.mean = 15 standard deviation = 6.

10. A data set had a mean of 5 and a standarddeviation of 2. 7 is added to each numberwithin this data set. What is the new mean andstandard deviation?

Answer Choices:mean = 5 standard deviation = 2.mean = 12 standard deviation = 2.mean = 5 standard deviation = 9.mean = 12 standard deviation = 9.









For questions 1 – 4, use the following data set to calculate the fivenumber summary.

A school in Springfield recorded the number of rain days per month for each month during the school year. Thedata are displayed below:

17 10 22 18 20 6 15 22 15

1. Based on thecollected data,what is the upper(or third) quartile ofthe number ofdays of rain for thegiven ninemonths?

Answer choices:12.5.17.21.22.

2. Based on thecollected data,what is the IQR(interquartile range)of the number ofdays of rain for thegiven ninemonths?

Answer choices:8.5.33.5.16.17.

3. What is the uppercutoff used todetermine if thereare any outliers inthis data set?

Answer choices:1.5 • (21 − 12.5).21 + 1.5 • (21 −12.5).21 • 1.5 • (21 −12.5).12.5 + 1.5 • (21 −12.5).

4. What percentageof the data fallsbetween 15.5 and21?

Answer choices:33.3%.66.6%.100%.50%.

To answer questions 5 – 8, use the following stemandleaf plot.

Suzanne recorded the amount of money she made in tips during the past two weeks. Her earnings are displayedbelow:

5. Based on the 6. The middle 50% of 7. The outliers in this 8. What is the cutoff



collected data,what is the lower(or first) quartile ofthe amount ofmoney Suzanneearned in tips?

Answer choices:24.28.37.48.

the data isbetween what twovalues?

Answer choices:24 and 37.28 and 48.37 and 82.27 and 48.

data set are:

Answer choices:62 and 82.just 62.There are nooutliers.just 82.

used to determineif there are any lowoutliers?

Answer choices:−2.2.24.30.

To answer questions 9 – 10, use the box plot below.

Molly wants to buy a new cell phone. Below is a box plot showing the prices of the phones for sale at a nearbystore:

9. What is the IQR of the phone price dataabove?


10. Are there any outliers in the phone price data?

Answer choices:There are no outliers.There is at least one above Q3.There is at least one below Q1.You cannot tell from the information provided.









For questions 1 – 2, use the following comparative stemandleaf plots to answer questions about the center,shape, and spread of two distributions.

Mr. Jones teaches two trigonometry classes. Below are the distributions of the most recent test scores of bothclasses.

1. Based on the collected data, the shape of thedistribution of the test scores of the 5thperiodclass would be best described as:

Answer choices:positively skewed.negatively skewed.symmetrical.bimodal.

2. Based on the collected data, the shape of thedistribution of the test scores of the 1stperiodclass would be best described as:



Mr. Jones teaches two trigonometry classes. Below are the distributions of the most recent test scores of bothclasses.



3. Based on the collecteddata, when comparing themean and the median testscores from the 5thperiodclass, what would be true?

Answer choices:mean = median.mean > median.mean < median.You cannot tell just bylooking at the plots.

4. Based on the collecteddata, which class had agreater spread of testscores?

Answer choices:1st period.5th period.They were the same.You cannot tell just bylooking at the plots.

5. Based on the collecteddata, which class had ahigher mean test score?

Answer choices:1st period.5th period.They were the same.You cannot tell just bylooking at the plots.

For questions 6 – 7, use the following comparative box plots to answer questions about the center, shape, andspread of two distributions.

The following box plots represent the amounts that the boys and girls in Mr. Jones's classes have spent on theirmost recent haircut:

6. Based on the collected data, the shape of thedistribution of the haircut costs for the boyscan be best described as:


7. Based on the collected data, the shape of thedistribution of the haircut costs for the girls canbe best described as:


For questions 8 – 10, use the following comparative box plots to answer questions about the center, shape, andspread of two distributions.

The following box plots represent the amounts that the boys and girls in Mr. Jones's classes have spent on theirmost recent haircut:



8. Based on the collecteddata, if you compare themedian haircut costs forboys and girls, what canyou conclude?

Answer choices:Boys had a higher mediancost.The median costs were thesame for boys and girls.Girls had a higher mediancost.You cannot tell just bylooking at the plots.

9. Based on the collecteddata, if you compare theboys' mean haircut cost totheir median haircut cost,what can you conclude?

Answer choices:mean > median.mean = median.mean < median.You cannot tell just bylooking at the plots.

10. Based on the collecteddata, if you compare themean haircut costs for boysand girls, what can youconclude?

Answer choices:Boys had a higher meancosts.Mean costs were the samefor boys and girls.Girls had a higher meancost.You cannot tell just bylooking at the plots.









For questions 1 – 3, find the yintercept of the linear regression line.

1. A data set has the followingpoints:

(2, 3), (4, 7), (6, 8)

The slope of the linearregression line is 1.25. Findthe yintercept of the linearregression.


(0, 2), (4, 1), (6, 0)



(1, 2), (5, 3), (7, 5)


For questions 4 – 7, predict the value of y given the linear regression equation.

4. A data set has aline of best fit withthe equation

. Whatdoes the equationpredict for a valueof x = 5?






.What does theequation predict fora value of x = 3?



For questions 8 – 10, find the residual of the point.

8. A data set has a line ofbest fit with the equation

. What is theresidual for the point (2, 7)?

9. A data set has a line of bestfit with the equation

. What is theresidual for the point (1, 6)?

10. A data set has a line of bestfit with the equation

. What isthe residual for the point(3, 11)?






2.7.1 Checkup: Descriptive Statistics PracticeProblems

Checkup


Answer the following questions using what you've learned from this unit. Write your responses in thespace provided.

Scoring: Each question is worth 5 points.

For questions 1 – 3, use the following stemandleaf plot to answer the questions.

1. How many elephants live atthe zoo?

Answer choices:421813There is not enoughinformation given to answerthis question.

2. What is the age differencebetween the oldest andyoungest elephants?

Answer choices:9224044

3. Which best describes theshape of the distribution ofages?

Answer choices:Positively skewedNegatively skewedRelatively symmetricalNormal


Brad Pit is a fabulous second baseman for the Portland Pilots baseball team. In his illustrious career he hascommitted the following number of errors each year:

4. Based on the collecteddata, what is the meannumber of errors Brad madeper year?

5. Based on the collecteddata, what is the modenumber of errors Bradcommitted during his ten

6. Based on the collecteddata, what is the mediannumber of errors Bradcommitted per year?



Answer choices:11.7121421

year career?




Mr. Johnson was concerned about the number of students absent from his classes during the day. He decidedto choose one week at random and tally the number of students who missed his classes each day. Here are hissample data:

7. Based on thecollected data,what is the rangeof number ofabsences per dayfrom this sample?

Answer choices:4810 12

8. Based on thecollected data,what is the meannumber ofabsences per dayfrom this sample?


9. Based on thecollected data,what is thevariance ofabsences per dayfrom this sample?

Answer choices:1.7923.24

10. Based on thecollected data,what is thestandard deviationof absences perday from thissample?

Answer choices:1.7923.24

For questions 11 – 14, use the following data set to calculate the fivenumber summary.

The Kingston High School girls' basketball team had a freethrow contest. Below are the number of free throwsin a row each member of the team made:

11. Based on thecollected data,what is the upper(or third) quartileof the number of

12. Based on thecollected data,what is the IQR(interquartilerange) of the

13. Based on thecollected data,what is the upperlimit cutoff todetermine if there

14. What percentageof the data fallsbetween 7 and 14consecutive freethrows?



consecutive freethrows made byeach player?


number ofconsecutive freethrows made byeach player?


are any outliers?

Answer choices:5 • (14 − 7)14 + 1.5 • (14 − 7)21 − 1.5 • (14 − 7)7 + 1.5 • (14 − 7)

Answer choices:25%50%75%100%


The school administration asked all boys and girls who went to the senior prom, "How much money did youspend on your dress or suit/tuxedo?" A sample of the results is shown below:

15. Based on the sample data,the shape of the distributionof the amount spent by theboys can best be describedas:


16. Based on the sample data,the shape of the distributionof the amount spent by thegirls can best be describedas:


17. Based on the sample data,if you compare the meanand the median amountsspent by the girls, what canyou conclude?

Answer choices:mean = medianmean > medianmean < medianYou cannot tell just bylooking at the plot.








For questions 1 – 3, determine whether the expression is a polynomial, and if so, find the degree of thepolynomial.

1. 2. 3.

For questions 4 – 5, factor the polynomial expression.

Calculation Tip: Find the GCF for each expression.

4. 16x 2 + 2x 5. 9x – 18x 2

For question 6, identify the operation(s) under which the described set is closed.

Calculation Tip: Create two integers or two polynomials and write an expression representing the sum,difference, product, or quotient.

6. integers

For questions 7 – 8, write the polynomial in descending order.

7. 8.

For questions 9 – 10, answer the question about the polynomial.

9. What is the coefficient of the term of degree 7in the polynomial below?

10. What is the coefficient of the term of degree 4in the polynomial below?






For questions 1 – 5, find the sum of the polynomials. Write your answers in descending order.

1. 2.

3. 4.

5.

For questions 6 – 10, find the difference of the polynomials. Write your answers in descending order.

6. 7.

8. 9.



10.









For questions 1 – 10, find the product of the binomials. Write your answer in descending order.

1. 2.

3. 4.

5. 6.

7. 8.

9. Talia has a square bedroom. Her family is 10. If Talia's old bedroom measured 10 feet by 10



moving and her bedroom in her new apartmentwill be 3 feet shorter in one direction and 5 feetlonger in the other direction. Write anexpression that represents the two binomialsyou would multiply together to find the area ofTalia's new bedroom.

feet, how much larger or smaller will her newbedroom be?









For questions 1 – 2, use the table to find the products of the two polynomials. Write your answer in descendingorder.

1. 2.

For questions 3 – 10, find the product of the two polynomials. Write your answer in descending order.

3. 4.

5. 6.



7. 8.

9. 10.









For questions 1 – 10, use long division to find the quotient. Write your answer in descending order.

1. 2. 3.

4. 5. 6.

7. 8.



9. 10.









For questions 1 – 2, identify the approximate solution(s) for the graphed system of polynomials.

Calculation Tip: Find the point(s) of intersection.

1. 2.

For questions 3 – 4, determine the number of solutions for the graphed polynomials.

Calculation Tip: Count the number of points of intersection.

3.

4.



For questions 5 – 10, answer the questions about the graphs of polynomials.

5. The equation and graph of a polynomial areshown below. The graph reaches its maximumwhen the value of x is 2. What is the yvalue ofthis maximum?

6. The equation and graph of a polynomial areshown below. The graph reaches its minimumwhen the value of x is 4. What is the yvalueof this minimum?

7. The points plotted below are on the graph of apolynomial. Between which two consecutive xvalues must the polynomial have a root?

Answer Choices: 6 to 53 to 22 to 11 to 0





3.8.1 Checkup: Polynomials Practice Problems Checkup



For questions 1 – 3, answer the questions about polynomials.

1. What is the degree of thepolynomial below?

2. What is the degree of thepolynomial below?

3. What is the coefficient of theterm of degree 6 in thepolynomial below?

For questions 4 – 9, find the sum or difference of the polynomials. Write your answer in descending order.

4. 5.

6. 7.

8. 9.



For questions 10 – 11, use the table to answer the questions. It is set up to multiply two polynomials.

10. What is the coefficient of the x 3term of theproduct?

11. What is the coefficient of the x 2term of theproduct?

For questions 12 – 14, find the product of the two polynomials. Write your answer in descending order.

12. 13.

14.

For questions 15 – 16, use long division to find the quotient. Write your answer in descending order.

15. 16.






For questions 1 – 3, choose the correct factorization of the polynomial.

1.

Answer Choices:

2.

Answer Choices:

3.

Answer Choices:

For questions 4 – 6, answer the questions about factors.

4. If the factors of apolynomial are x + 1 andx 6, what values of xmake the polynomial 0?

5. If the factors of apolynomial are x + 3 andx + 2, what values of xmake the polynomial 0?

6. If the factors of apolynomial are x + 8 andx 4, what values of xmake the polynomial 0?

For questions 7 – 10, find the solutions to the equation.

7. 8.



9. 10.









For questions 1 – 10, use the tiles to find the factorization of the polynomial.

1. 2.

3. 4.

5. 6.



7. 8.

9. 10.






For questions 1 – 10, write the factorization of the polynomial in the graph. Assume the polynomial has noconstant factor.

1. 2.

3. 4.

5. 6.



7. 8.

9. 10.






For questions 1 – 10, use the grouping method to factor the polynomial completely.

1. 2. 3.

4. 5. 6.

7. 8.

9. 10.









For questions 1 – 10, factor the trinomial.

1. 2. 3. 4.

5. 6. 7. 8.

9. 10.










1. 2. 3.

4. 5. 6.


7. 8. 9. 10.









For questions 1 – 10, factor the expression.

1. 2. 3. 4.

5. 6. 7. 8.

9. 10.






4.8.1 Checkup: Factoring of Polynomials PracticeProblems

Checkup



For questions 1 – 2, use the tiles to factor the polynomials.

1. The picture below shows the factorization of . Write the factorization.

2. The picture below shows the factorization of . Write the factorization.

For questions 3 – 4, use the graphs to find each factorization.

3. Use the graph to find the factorization of .

4. Use the graph to find the factorization of .



For questions 5 – 8, factor the polynomial expressions.

5. 6. 7. 8.

For questions 9 – 14, factor each polynomial.

9. 10. 11.

12. 13. 14.

For questions 15 – 16, find the solutions to each equation.

15. 16.






For questions 1 – 4, find the answer choice that could be the equation of the parabola.

1. The vertex of this parabola is at the origin.Which of the answer choices could be itsequation?

Answer Choices:

2. The vertex of this parabola is at (1, 3). Whichof the answer choices could be its equation?

Answer Choices:





Answer Choices: Answer Choices:

For questions 5 – 7, determine the coefficient of the squared term in the equation for the parabola.

5. The vertex of this parabolais at (2, 4). When the xvalueis 3, the yvalue is 4.5. Whatis the coefficient of thesquared term in the equationof this parabola?

6. The vertex of this parabolais at (1, 2). When the xvalueis 0, the yvalue is 0. Whatis the coefficient of thesquared term in the equationof this parabola?

7. The vertex of this parabolais at (1, 4). When the yvalueis 5, the xvalue is 4. Whatis the coefficient of thesquared term in the equationof this parabola?



For questions 8 – 10, write the equation of the parabola in standard form.

8. 9. 10.









For questions 1 – 7, find all the solutions to the equation.

1. 2. 3.

4. 5.

6. 7.



For questions 8 – 10, find all the solutions of the equation.

8. 9. 10.









For questions 1 – 4, determine what number you should add to the equation to complete the square.

1. 2. 3. 4.

For questions 5 – 10, solve the equation by completing the square and then solving for x.

5. 6.

7. 8.

9. 10.






Formula

Quadratic Formula:

For questions 1 – 6, use the quadratic formula to find the solutions to each equation.

1. 2. 3.

4. 5. 6.



For questions 7 – 10, find the roots of each polynomial using the quadratic formula.

7. 8.

9. 10.






For questions 1 – 3, find the xintercepts of the function.

1. 2. 3.

For questions 4 – 6, find the vertex of the function given below.

4. 5. 6.



For questions 7 – 10, determine which function is graphed.

7.

Answer Choices:

8.

Answer Choices:

9.

Answer Choices:

10.

Answer Choices:






For questions 1 – 4, determine the number of solutions to the system of nonlinear equations.

1. 2.

3. 4.

For questions 5 – 7, write the variable in isolated form.

5. Write in isolated form. 6. Write in isolated form. 7. Write in isolated form.



For questions 8 – 10, find all the solutions for x.

8. 9. 10.









For questions 1 – 2, compare the slopes of the graphs.

1. Describe how the slopes of the graphed functionsdiffer.

2. Describe how the slopes of the graphed functionsdiffer.

For questions 3 – 5, compare the graphs of the equations.

3. Describe the similarities and differences in the graphs of the equations y = −9x and y = 4x + 2



4. Describe the similarities and differences in the graphs of the equations and

5. Describe the similarities and differences in the graphs of the equations and .

For questions 6 – 7, find the intercepts of each function.

6. Identify the x and yintercepts of the graph of thefunction y = −3x + 6.

7. Identify the x and yintercepts of the graph of thefunction y = 2x 2 + 14x + 20.



For questions 8 – 10, identify key features of the graph of each equation.

8. Identify key features of the graph of the equation

.

9. Identify key features of the graph of the equation .

10. Identify key features of the graph of the equation






5.8.1 Checkup: Quadratic Equations and FunctionsPractice Problems

Checkup



Formula

Quadratic formula:

For question 1, solve the equation by factoring.

1. y =

For questions 2 – 4, use the quadratic formula to find the solutions to each equation.

2. 3.



4.









For questions 1 – 8, find , the inverse of .

1. 2. 3. 4.

5. 6. 7. 8.

For questions 9 – 10, answer the question about inverses.

9. The function below relates the distance(measured in miles) Bob can drive his rentalcar and the amount of money (in dollars) it willcost.

It takes as input the number of dollars spentand returns as output the number of milesdriven.

Write the equation that represents the inverse

10. The function below relates the area of atriangle with a given base of 7 and the heightof the triangle.

It takes as input the height of the triangle andreturns as output the area of the triangle.

Write the equation that represents the inversefunction , which takes the triangle's areaas input and returns the height of the triangle.



function , which takes the number ofmiles driven as input and returns the number ofdollars owed.









For questions 1 – 2, use each mapping diagram to write ordered pairs found in the inverse function.

1. 2.

For questions 3 – 4, identify three ordered pairs found on the graph of the inverse of each graphed functionbelow.

3. 4.



For questions 5 – 6, write the equation of the inverse of each function. Sketch a graph of the inverse.

5. 6.

For questions 7 – 10, determine whether the inverse of is a function.

7. 8.

9. 10.






For questions 1 – 4, write the correct parent function.

1.What is the linearparent function?

2.What is the quadraticparent function?

3.What is the absolutevalue parent function?

4.What is the reciprocalparent function?

For questions 5 – 8, choose the correct parent function.

5. Which parent function is represented by thegraph?

Answer choices:Linear parent functionQuadratic parent functionAbsolute value parent functionReciprocal parent function









For questions 9 – 10, answer each questions about the graphs of parent functions.

9. Which parent function does not have a graphthat goes through the origin?


10. Which parent function has a graph that is aparabola?










For questions 1 – 10, write the equation of the graph.

1. The graphs below have the same shape. Writethe equation of .







6. The graph below has the same shape as , but it is shifted 4 units to the right.

Write the equation for .



9. If were shifted 2 units to the left

and 3 units up, what would the new equationbe?

10. If were shifted 5 units to the

right and 2 units down, what would the newequation be?






For questions 1 – 10, Find the equation for .

1. The graph of , shown below, resembles

the graph of , but it has been

changed somewhat. Which of the followingcould be the equation of ?

Answer Choices:




Answer Choices:









Answer Choices: Answer Choices:




Answer Choices:




Answer Choices:






Answer Choices:




Answer Choices:








Answer Choices:


Answer Choices:









For questions 1 – 2, shift the parent function up or down.

1. If you shift the linear parent function, F(x) = x,up 6 units, what is the equation of the newfunction?

2. If you shift the quadratic parent function, F(x) =

x 2, down 10 units, what is the equation of thenew function?

For questions 3 – 4, shift the parent function left or right.

3. If you shift the absolute value parent function,F(x) = |x|, left 4 units, what is the equation ofthe new function?

4. If you shift the reciprocal parent function,

F(x) = , right 2 units, what is the equation of

the new function?

For questions 5 – 6, vertically stretch or compress the parent function.

5. If you vertically stretch the linear parentfunction, F(x) = x, by multiplying by 8, what isthe equation of the new function?

6. If you vertically compress the quadratic parent

function, F(x) = x 2, by multiplying by , what

is the equation of the new function?

For questions 7 – 8, flip the parent function across the x or yaxis.

7. If you flip the absolute value parent function, F(x) = |x|, across the yaxis, what is the equationof the new function?

8. If you flip the reciprocal parent function,

F(x) = , across the xaxis, what is the



equation of the new function?

For questions 9 – 10, combine stretching or compressing with shifting.

9. If you apply the changes below to the linearparent function, F(x) = x, what is the equationof the new function?

Vertically compress by multiplying by .

Flip over the xaxis.

10. If you apply the changes below to the

quadratic parent function, F(x) = x 2, what isthe equation of the new function?

Shift 7 units right.

Shift 3 units up.






6.7.1 Checkup: Undoing Functions and Moving ThemAround Practice Problems

Checkup



For questions 1 – 2, answer the questions about inverting functions.

1. If (3, 5) is an ordered pair of the function F(x),which of the following must be an ordered pairof the inverse of F(x)?

Answer Choices:

(3, 5)(3, 5)(5, 3)(5, 3)

2. If (2, 3) is an ordered pair of the function F(x),which of the following must be an ordered pairof the inverse of F(x)?

Answer Choices:

(3, 2)(2, 3)(2, 3)(3, 2)

For questions 3 – 6, find F 1(x), the inverse of F(x).

3. F(x) = x – 10 4. 5. F(x) = 3x + 7 6. F(x) = 8x



For questions 7 – 10, determine whether the inverse of F(x) is a function.

7. 8.

9. 10.

For questions 11 – 16, write the equation for F(x).

11. The graph of F(x), shown below, has the sameshape as the graph of but is shifted

up by 3 units. Write the equation for F(x).


left by 4 units. Write the equation for F(x).



.


right by 5 units. Write the equation for F(x).

14. The graph of F(x), shown below, has the sameshape as the graph of but is

shifted right by 2 units. Write the equation for F(x).


right by 3 units and down by 2 units. Write theequation for F(x).

16. The graph of F(x), shown below with a dashedline, has the same shape as the graph of

, shown with a solid line. Write the

equation for F(x).




17. The graph of F(x), shown below, has the sameshape as the graph of but is flipped

over the xaxis. Write the equation for F(x).


flipped over the xaxis. Write the equation for F(x).



stretched to be 5 times as tall. Write theequation for F(x).


stretched to be twice as tall. Write the equationfor F(x).