Question

select the zeros of $g(x) = -4x^4 + 8x^3 + 60x^2$.
identify the graph of the function.

Explanation:

Step1: Factor out common term

$g(x) = -4x^2(x^2 - 2x - 15)$

Step2: Factor quadratic expression

$g(x) = -4x^2(x-5)(x+3)$

Step3: Solve for zeros (set $g(x)=0$)

$-4x^2=0 \implies x=0$; $x-5=0 \implies x=5$; $x+3=0 \implies x=-3$

Step4: Analyze end behavior

Leading term: $-4x^4$, as $x\to\pm\infty$, $g(x)\to-\infty$

Step5: Match zeros and end behavior

Zeros at $x=-3, 0, 5$; ends point downward. The bottom-left graph matches this.

Answer:

Zeros: $x=-3$, $x=0$, $x=5$
Graph: The bottom-left graph (curves downward at both ends, crosses/touches x-axis at $x=-3$, $x=0$, $x=5$)