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13.3 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

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Presentation on theme: "13.3 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square."— Presentation transcript:

1 13.3 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square

2 Steps to complete the square
1.) 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 + 6x
3 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 To solve by completing the square
If a quadratic equation does not factor we can solve it by two different methods 1.) Completing the Square (today’s lesson) 2.) Quadratic Formula (Monday’s lesson)

6 Steps to solve by completing the square
1.) If the quadratic does not factor, move the constant to the other side of the equation Ex: x²-4x -7 = 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 /2= 2²=4 3.) Add the number you got to complete the square to both sides of the equation Ex: x² -4x +4 = 7 +4 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

7 Solve by Completing the Square
+9

8 Solve by Completing the Square
+121

9 Solve by Completing the Square
+1

10 Solve by Completing the Square
+25

11 Solve by Completing the Square
+16

12 Solve by Completing the Square
+9

13 The coefficient of x2 must be “1”

14 The coefficient of x2 must be “1”

15

16 Assignment Page 588 (2-32) even


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