5.4 – Completing the Square

Objectives: Use completing the square to solve a quadratic

equation. Use the vertex form of a quadratic function to locate the axis of symmetry of its graph.

Standard: 2.8.11.N. Solve quadratic equations symbolically and graphically

Example 1

Example 1 c and d

c. x2 – 7xThe coefficient of x is

-7½ (-7) = Thus the perfect

square trinomial is

2

7

2

2

7

222

2

7

2

77

xxx

22

2

77

xx

d. x2 + 16xThe coefficient of x is

16½ (16) = 8 (8)2 =

64Thus the perfect

square trinomial is 22 86416 xxx

64162 xx

Solving Equations by Completing the Square

STEPS: Make sure A = 1. Bring the C to the Zero side. Complete the Square meaning “ take ½ of B and

Square It.” Add the answer you got from complete the

square on the other side so you keep the equation balanced.

Put the complete the square side into perfect square notation.

Solve the equation.

Example 2a

Example 2b *

x2 + 10x – 24 = 0

Example 2c *

2x2 + 6x = 7

Example 2d *

3x2 – 6x = 5

VERTEX FORMVertex FormIf the coordinates of the vertex of the graph of y = ax2 +

bx + c, where a ≠ 0, are (h,k), then you can represent the parabola as y = a(x – h)2 + k, which is the vertex form of a quadratic equation.

Another Vertex Form Problem!

Given g(x) = 3x2 – 9x – 2, write the function in vertex form, and give the coordinates of the vertex and the equation of the axis of symmetry. Then describe the transformations from f(x) = x2 to g.

Writing Questions

HomeworkPg. 304 #12-46 even