1. 4.7 – Complete the Square
In lesson 4.5, you solved equations of the form x2 = k by finding the square roots. This method also works if one side of an equation is a perfect square trinomial.

2. 4.7 – Complete the Square
Example 1a:
Solve x2 – 8x + 16 = 25

3. 4.7 – Complete the Square
Example 1b:
Solve x2 – 2x + 1 = 144

4. Example 1c: Solve 9x2 – 12x + 4 = -3
4.7 – Complete the Square
Example 1c:
Solve 9x2 – 12x + 4 = -3

5. 4.7 – Complete the Square
In the first three examples, the trinomials were perfect squares. Sometimes you need to add a term to an expression x2 + bx to make it a square. This process is called completing the square.

6. 4.7 – Complete the Square

7. 4.7 – Complete the Square Example 2a:
Find the value that makes x2 + 16x + c a perfect square trinomial. Then write the expression as the square of a binomial.

8. 4.7 – Complete the Square Example 2b:
Find the value that makes x2 + 12x + c a perfect square trinomial. Then write the expression as the square of a binomial.

9. 4.7 – Complete the Square Example 2c:
Find the value that makes x2 - 13x + c a perfect square trinomial. Then write the expression as the square of a binomial.

10. 4.7 – Complete the Square
Example 3a:
Solve x2 – 12x + 4 = 0

11. 4.7 – Complete the Square
Example 3b:
Solve x2 – 10x + 1 = 0

12. 4.7 – Complete the Square
Example 4a:
Solve 2x2 + 8x + 14 = 0

13. 4.7 – Complete the Square
Example 4b:
Solve 3x2 + 12x - 18 = 0

14. 4.7 – Complete the Square
Example 4c:
Solve 2x2 + 10x +17 = 0

15. Write y = x2 – 10x + 22 in vertex form. Then identify the vertex.
4.7 – Complete the Square
Example 5a:
Write y = x2 – 10x + 22 in vertex form. Then identify the vertex.

16. Write y = 2x2 + 24x + 25 in vertex form. Then identify the vertex.
4.7 – Complete the Square
Example 5b:
Write y = 2x2 + 24x + 25 in vertex form. Then identify the vertex.

17. Find the maximum height of the baseball
4.7 – Complete the Square
Example 6:
The height y (in feet) of a baseball t seconds after it is hit is given by this function:
y = -16t2 + 96t + 3.
Find the maximum height of the baseball