1 Do Now Factor the expression. x2 + 18x + 81 x2 - 22x + 121

2 Objective: solve quadratic equations by completing the square

3 Completing the Square Find the value of c that makes x2 - 6x + c a perfect square trinomial. Then write the expression as the square of a binomial. To find the value of c, use the “b” value (ax2+bx+c): Find half the coefficient of x. Square the result of Step 1. Replace c with the result of Step 2. Answer: ½ (– 6) = (– 3)2 = x2 – 6x + 9 when c = 9, x2 – 6x + 9 = (x – 3)2

4 Example: Completing the SquareFind the value of c that makes x2 - 12x + c a perfect square trinomial. Then write the expression as the square of a binomial. To find the value of c, use the “b” value (ax2+bx+c): Find half the coefficient of x. Square the result of Step 1. Replace c with the result of Step 2. Answer:

5 Practice Find the value of c that makes the expression a perfect square trinomial. Then write the expression as the square of a binomial. x2 + 8x + c x2 - 14x + c x2 - 10x + c x2 + 18x + c

6 Solving Quadratics

7 Example

8 Solve the equation by completing the square.x2 + 2x – 3 = 0 x2 - 6x + 16 = 0

9 Solve the equation by completing the square.x2 - 8x - 20 = 0 x2 + 4x - 15 = 21

10 Solve the equation by completing the square.x2 - 2x - 2 = 0 x2 + 6x + 3 = 0

11 Homework Completing the Square Worksheet