1 Chapter 4: Quadratic Functions and EquationsSection 4.6: Completing the Square

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

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

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

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

8 Section 4.6: Completing the SquareIn 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 SquareExamples: 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 SquareYou 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 SquareSolving an Equation by Completing the Square

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

14 Section 4.6: Completing the SquareWhen 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 SquareYou 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 SquareHomework (Part 2): Pg. 237 #28-44 (even)

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

19 Section 4.6: Completing the Square3. Write each equation in vertex form. Then analyze the function. y = x2 + 8x – 3

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