Question

f(x) = -(x + 2)(x - 2)^2(x - 7)
plot the y-intercept and the roots. click on the graph to plot a point. click a point again to delete it.
done plotting

Explanation:

Step1: Find x-intercepts (roots)

Set $f(x)=0$, solve $-(x+2)(x-2)^2(x-7)=0$.
Roots are $x=-2$, $x=2$ (double root), $x=7$.
Corresponding points: $(-2,0)$, $(2,0)$, $(7,0)$.

Step2: Find y-intercept

Set $x=0$, calculate $f(0)$.

$$\begin{align*} f(0)&=-(0+2)(0-2)^2(0-7)\\ &=-(2)(4)(-7)\\ &=56 \end{align*}$$

Corresponding point: $(0,56)$.

Answer:

Roots (x-intercepts): $(-2, 0)$, $(2, 0)$, $(7, 0)$
y-intercept: $(0, 56)$