Question

graph the polynomial function f(x)=x^2(x + 3) using (parts (a) through (e)). the lesser zero of the function is of multiplicity 1, so the graph of f crosses the x - axis at x=-3. the greater zero of the function is of multiplicity 2, so the graph of f touches the x - axis at x = 0. (d) determine the maximum number of turning points on the graph of the function. (type a whole number.)

Explanation:

Step1: Recall the formula for the number of turning - points of a polynomial

The maximum number of turning points of a polynomial function \(y = f(x)\) of degree \(n\) is given by \(n - 1\).

Step2: Determine the degree of the polynomial \(f(x)=x^{2}(x + 3)\)

First, expand \(f(x)=x^{2}(x + 3)=x^{3}+3x^{2}\). The degree \(n\) of the polynomial \(f(x)=x^{3}+3x^{2}\) is 3.

Step3: Calculate the maximum number of turning points

Using the formula \(n - 1\), with \(n = 3\), we have \(3-1=2\).

Answer:

2