Completing the Square

1. Completing the Square Section 5.4

2. -

3. -

4. -

5. -

6. Ex. • -

7. Solve by completing the square

8. Solve by completing the square

9. Day 2 Vertex form • The coordinates of the vertex of the graph • where are (h,k) then the parabola can be written as • which is called the vertex form of a quadratic function.

10. The axis of symmetry is a line that divides the parabola into two parts that are mirror images of each other. • The axis of symmetry passes through the vertex of the parabola. x = ?

11. Review transformations from chapter 2 • If y = f(x), then • y = af(x) is a vertical stretch or compression of f • y = f(bx) is a horizontal stretch or compression of f • y = f(x) + k is a vertical translation of f • y = (x – h) is a horizontal translation of f.

12. Given h(x) = write the function in vertex form and give the coordinates of the vertex and the equation of the axis of symmetry. Then describe the transformation from f(x) = to h. • Step 1 Write in vertex form. • h(x) = - factor GCF from the first 2 terms • h(x) =

13. Complete the square. h(x) = • h(x) = 2(x2 + 8x + 16) + 23 – 2(16) • h(x) = 2(x + 4)2 – 9 • Coordinates of vertex (-4, -9) • The axis of symmetry: x = -4 • Translations: vertical stretch of 2, horizontal translation 4 units to the left, and vertical translation 9 units down.

14. A softball is thrown upward at an initial velocity of 32 ft per second from 5 feet above the ground. The ball’s height in feet above the ground is modeled by h(t) = -16t2 + 32t + 5, where t is the time in seconds after the ball is released. Complete the square and find the maximum height of the ball.

15. Each side of a square is increased by 2 cm, producing a new square whose area is 30 cm2. Find the length of the sides of the original square.