Academy Algebra II

1. Academy Algebra II 5.9: Write Polynomial Functions and Models HW: p.397 (4, 6), p.399 (#13)

2. Write a cubic function whose graph passes through the points. 1.) (-4, 0), (0, -6), (1, 0), (3, 0)

3. Write a cubic function whose graph passes through the points. 2.) (-2, 0), (-1, 0), (0, -8), (2, 0)

4. The table shows the typical speed y (in feet per second) of a space shuttle x seconds after launch. Find a polynomial model for the data. Use the model to predict the time when the shuttle’s speed reaches 4400 feet per second, at which point its booster rockets detach.

5. Do Now: Find the x-intercepts of the functions. f(x) = 1/6(x + 3)(x – 2)2

6. Academy Algebra II 5.8: Analyze Graphs of Polynomial Functions HW: p.390 (4-10 even, 16, 20), p.391 (22, 24)

7. Turning Points of a Graph • The graph of every polynomial function of degree n has at most n – 1 turning points. If the polynomial has n distinct real zeros, then its graph has exactly n – 1 turning points. • Turning points correspond to a local maximum or local minimum of the function.

8. Graph the function. Label the zeros, y-intercepts, and additional points in-between the zeros. • f(x) = 1/6(x + 3)(x – 2)2

9. Graph the function. Label the zeros, y-intercepts, and additional points in-between the zeros. • f(x) = 4(x + 1)(x + 2)(x – 1)

10. Use the graphing calculator to graph the polynomial function. Identify the x-intercepts and any local maximum or minimum points. • f(x) = x4 – 6x3 + 3x2 + 10x – 3

11. Use the graphing calculator to graph the polynomial function. Identify the x-intercepts and any local maximum or minimum points. • f(x) = x5 – 4x3 + x2 + 2