Quadratic Function

Solving Quadratic Equations Algebraically

There are four basic methods to solve quadratic equations algebraically.

•Factoring •Extracting Square Roots •Completing the Square •Using the Quadratic Formula

Solve Graphically

Equations Graphically: When solving equations graphically we are trying to find

where the graph crosses or touches the x‐axis. These places are the x‐intercepts where y = 0.

If we have the equation y = 2x – 4 and we want to solve graphically, we will graph this equation and find where the line intercepts the x‐axis.

Ex. By viewing the graph, we can see x = 2 when y = 0, therefore x = 2 is a solution.

Rules for factoring

1. Set the equation equal to zero.

2. Factor.3. Set each factor equal to

zero.

Examples

Example 2

Example 3

Steps for solving using square roots.

1. Get the squared term alone on one side. Move the constants to the other side.

2. Take the square root of each side. Remember plus and minus.

3. Finish solving for x.

Example 1

Example 2

Example 3

Steps for completing the square.

Example 1

Example 2

Example 3

Complex Solutions of Quadratic Equations

Use the quadratic formula to solve.

2 4

2

b b acx

a

Solve absolute values using the grapher.

In the book, always go to what is reasonable. If you are not sure, solve to the hundredths.

The End