Question

graph the polynomial function f(x)=x^2(x + 3) using parts (a) through (e). comma to separate answers as needed. type each answer only once.) the y - intercept is 0. (simplify your answer. type an integer or a fraction.) (c) determine the zeros of the function and their multiplicity. use this information to determine whether the graph crosses or touches the x - axis at each x - intercept. the zero(s) of f is/are . (simplify your answer. type an integer or a fraction. use a comma to separate answers as needed. type each answer only once.)

Explanation:

Step1: Set the function equal to 0

Set $f(x)=x^{2}(x + 3)=0$.

Step2: Use the zero - product property

If $ab = 0$, then either $a=0$ or $b = 0$. So we have $x^{2}=0$ or $x+3=0$.

Step3: Solve for x

For $x^{2}=0$, we get $x = 0$ (with multiplicity 2 since the exponent of $x$ is 2). For $x+3=0$, we get $x=-3$ (with multiplicity 1).

Answer:

$0,-3$