Answer Box

Answer to Question 8

The polynomial function P(x) = x³ - 25x.
a) Factor and determine the roots.
P(x) = x³ + 25x = x(x² - 25). Roots are 0, ±5.
b) Determine the end behavior of the graph.
The function has an odd degree and the leading coefficient is positive. The means the end behaviors will be left down, right up.
c) Make a sketch of the graph.

Since the equation is given, you can use test points to enhance your sketch.
Testing the point x = -3, showed that the test point x = -2 was not a relative maximum location on this graph.
With the graph being degree 3, there will be at most 2 turning points.