1. Chapter 4: Quadratic Functions and Equations
Section 4.6: Completing the Square

2. Section 4.6: Completing the Square
Goal: To solve equations by completing the square and to rewrite functions by completing the square

3. Section 4.6: Completing the Square
In Section 4.5 we learned how to solve quadratic equations by factoring
In some cases, when there is no x term in an equation, a solution can be found by solving for x2 and taking the square root
Ex:
3x = 123

4. Section 4.6: Completing the Square
Examples:
1. What is the solution of each equation?
A) 3x2 + 5 = 20 B) 8x2 – 3 = 29

5. Section 4.6: Completing the Square
Solving a Perfect Square Trinomial Equation: if an expression is perfect square trinomial, the equation can be solved using square roots.
Solve x2 + 14x + 49 = 64

6. Section 4.6: Completing the Square
You try:
2. What is the solution of x2 + 12x + 36 = 9 ?
3. Solve x2 – 10x + 25 = 12

7. Section 4.6: Completing the Square
Homework (Part 1) : Pg. 237 #12-26 (even)

8. Section 4.6: Completing the Square
In Section 4.5 there were problems that would not factor
A process known as Completing the Square will make every equation or expression factorable
Use this process if there is both an x2 term and an x term and if the expression/equation will not factor

9. Section 4.6: Completing the Square

10. Section 4.6: Completing the Square
Examples:
1. Find the value of c that make x2 + 16x + c a perfect square. Then write the trinomial as a perfect square.

11. Section 4.6: Completing the Square
You try:
2. What value completes the square for x2 + 14x + c ? Write the trinomial as a perfect square.
3. What value completes the square for x2 – 5x + c ? Write the trinomial as a perfect square.

12. Section 4.6: Completing the Square
Solving an Equation by Completing the Square

13. Section 4.6: Completing the Square
Example:
4. Solve the quadratic equation by completing the square:
x2 + 4x – 12 = 0

14. Section 4.6: Completing the Square
When the coefficient of the quadratic term is not 1, you must divide the equation by that coefficient before completing the square.
Example:
5. Solve 3x2 – 2x – 1 = 0 by completing the square

15. Section 4.6: Completing the Square
You try:
6. What is the solution of 3x2 + 18x – 3 = 0 ?
7. What is the solution of x2 – 10x = -2x + 5

16. Section 4.6: Completing the Square
Homework (Part 2): Pg. 237 #28-44 (even)

17. Section 4.6: Completing the Square
Writing a quadratic in Vertex Form:
Similar process to completing the square, however, instead of adding to both sides of the equals, need to “undo” on the same side of the equals
Example:
1. Write each equation in vertex form. Then analyze the function.
y = x2 + 2x + 4

18. Section 4.6: Completing the Square
Example:
2. Write each equation in vertex form. Then analyze the function.
y = -2x2 – 4x + 2

19. Section 4.6: Completing the Square
3. Write each equation in vertex form. Then analyze the function. y = x2 + 8x – 3

20. Section 4.6: Completing the Square
Homework (Part 3): Pg. 238 #46-51 (all)