Question

graph the polynomial function f(x)=(x + 1)(x - 3)(x + 4) using parts (a) through (e). comma to separate answers as needed. type each answer only once.) the least zero is a zero of multiplicity 1, so the graph of f crosses the x - axis at x=-4. the middle zero is a zero of multiplicity 1, so the graph of f crosses the x - axis at x=-1. the greatest zero is a zero of multiplicity 1, so the graph of f crosses the x - axis at x=3. (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 maximum 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

Expand $f(x)=(x + 1)(x - 3)(x + 4)$. First, $(x + 1)(x - 3)=x^{2}-3x+x - 3=x^{2}-2x - 3$. Then $(x^{2}-2x - 3)(x + 4)=x^{3}+4x^{2}-2x^{2}-8x-3x - 12=x^{3}+2x^{2}-11x - 12$. The degree $n = 3$.

Step3: Calculate the maximum number of turning points

Using the formula $n - 1$, with $n = 3$, we have $3-1 = 2$.

Answer:

2