1 Solve Quadratic Functions by Completing the SquareObjective: To complete a square for a quadratic equation and solve by completing the square

2 Steps to complete the square1.) You will get an expression that looks like this: AX²+ BX 2.) Our goal is to make a square such that we have (a + b)² = a² +2ab + b² 3.) We take ½ of the X coefficient (Divide the number in front of the X by 2) 4.) Then square that number

3 To Complete the Square x2 + 6x3 Take half of the coefficient of ‘x’ Square it and add it 9 x2 + 6x + 9 = (x + 3)2

4 Complete the square, and show what the perfect square is:

5 Steps to solve by completing the square1.) If the quadratic does not factor, move the constant to the other side of the equation Ex: x²-4x -7 =0 x²-4x=7 2.) Work with the x²+ x side of the equation and complete the square by taking ½ of the coefficient of x and squaring Ex. x² -4x 4/2= 2 2²=4 3.) Add the number you got to complete the square to both sides of the equation Ex: x² -4x +4 = )Simplify your trinomial square Ex: (x-2)² =11 5.)Take the square root of both sides of the equation Ex: x-2 =±√11 6.) Solve for x Ex: x=2±√11

6 Solve by Completing the Square+9

7 Solve by Completing the Square+121

8 Solve by Completing the Square+1

9 Solve by Completing the Square+25

10 Solve by Completing the Square+16

11 Solve by Completing the Square+9

12 The coefficient of x2 must be “1”

13 The coefficient of x2 must be “1”

14