1. Warm-Up Factor. 6 minutes 1) x 2 + 14x + 49 2) x 2 – 22x + 121 3) x 2 – 12x - 64 Solve each equation. 4) d 2 – 100 = 0 5) z 2 – 2z + 1 = 0 6) t 2 + 16 = -8t

2. Completing the Square Completing the Square Completing the Square Objectives: Use completing the square to solve a quadratic equation

3. Example 1 Complete the square for each quadratic expression to form a perfect-square trinomial. a) x 2 – 10x find x 2 – 10x + 25 (x - 5) 2 b) x 2 + 27x find

4. Practice 1) x 2 – 7x2) x 2 + 16x Complete the square for each quadratic expression to form a perfect-square trinomial. Then write the new expression as a binomial squared.

5. Example 2 Solve x 2 + 18x – 40 = 0 by completing the square. x 2 + 18x = 40 find x 2 + 18x + 81 = 40 + 81 (x + 9) 2 = 121 x = 2 or x = -20

6. Example 3 Solve 3x 2 - 6x = 5 by completing the square. 3(x 2 - 2x) = 5 find 3(x 2 - 2x + 1) = 5 + 3 3(x - 1) 2 = 8

7. Practice Solve by completing the square. 1) x 2 + 10x – 24 = 0 2) 2x 2 + 10x = 6

8. Warm-Up Solve each equation by completing the square. 1) x 2 + 10x + 16 = 0 2) x 2 + 2x = 13

9. Completing the Square Completing the Square Objectives: Use the vertex form of a quadratic function to locate the axis of symmetry of its graph

10. Transformations y = af(x) gives a vertical stretch or compression of f y = f(ax) gives a horizontal stretch or compression of f y = f(x) + k gives a vertical translation of f y = f(x - k) gives a horizontal translation of f

11. Vertex Form If the coordinates of the vertex of the graph of y = ax 2 + bx + c, where are (h,k), then you can represent the parabola as y = a(x – h) 2 + k, which is the vertex form of a quadratic function.

12. Example 1 Write the quadratic equation in vertex form. Give the coordinates of the vertex and the equation of the axis of symmetry. y = -6x 2 + 72x - 207 y = -6(x 2 - 12x) - 207 y = -6(x 2 - 12x y = -6(x - 6) 2 + 9 vertex: (6,9) axis of symmetry: x = 6 + 36)– 207+216 vertex form: y = a(x – h) 2 + k

13. Example 2 Given g(x) = 2x 2 + 16x + 23, write the function in vertex form, and give the coordinates of the vertex and the equation of the axis of symmetry. Then describe the transformations from f(x) = x 2 to g. g(x) = 2x 2 + 16x + 23 = 2(x 2 + 8x) + 23 = 2(x 2 + 8x = 2(x + 4) 2 - 9 = 2(x – (- 4)) 2 + (-9) + 16)+ 23– 32 vertex: (-4,-9) axis of symmetry: x = -4 vertex form: y = a(x – h) 2 + k

14. Practice Given g(x) = 3x 2 – 9x - 2, write the function in vertex form, and give the coordinates of the vertex and the equation of the axis of symmetry. Then describe the transformations from f(x) = x 2 to g.

15. Homework