Analyze polynomial function... f(x)=(x+7)(x-5)^2

Question

f(x)=(x+7)(x-5)^2

A) the graph of F behaves like y = ___ for large values of |x|

B) determine maximum number of turning points on the graph of the function

Answer 1

behaves like x^3 (the leading term)

a cubic can have up to 2 turning points.

Because there are zeroes at -7 and 5, there is a turning point between them. Because 5 is a double root, it is also a turning point. Thus, we have our two turning points.