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

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

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

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. x y

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

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

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.

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

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

Use the graphing calculator to graph the polynomial function. Identify the x-intercepts and any local maximum or minimum points. f(x) = x 4 – 6x 3 + 3x x – 3

Use the graphing calculator to graph the polynomial function. Identify the x-intercepts and any local maximum or minimum points. f(x) = x 5 – 4x 3 + x 2 + 2