Question

algebra 2 362403 - 6 fy - 1
benchmark test 2
the graph of function f is shown. use the zeros and the turning points of the graph. what is the rule for f?
a. $f(x)=x^{3}+2x^{2}+12x$
b. $f(x)=x^{3}+x^{2}-12x$
c. $f(x)=x^{3}+\frac{1}{2}x^{2}-x - 12$
d. $f(x)=x^{3}-x^{2}+12x$

Explanation:

Step1: Identify zeros from graph

Zeros at $x=-4$, $x=0$, $x=3$

Step2: Write factored form

$f(x)=x(x+4)(x-3)$

Step3: Expand the factors

First multiply $(x+4)(x-3)$:
$x(x^2 -3x +4x -12) = x(x^2 +x -12)$

Step4: Distribute the $x$ term

$x^3 +x^2 -12x$

Step5: Match to options

Result matches option B

Answer:

B. $f(x) = x^3 + x^2 - 12x$