Question

select the correct answer:which equation could represent this graphed cubic function?$\bigcirc f(x)=(x-2)^2(x+1)$$\bigcirc f(x)=(x+2)(x-1)$$\bigcirc f(x)=(x+2)^2(x-1)$$\bigcirc f(x)=(x+2)(x+4)(x-1)$

Explanation:

Step1: Identify x-intercepts

From the graph, the x-intercepts are $x=-2$ (touching, so even multiplicity) and $x=1$ (crossing, so odd multiplicity).

Step2: Match to options

Check each option:

• $f(x)=(x-2)^2(x+1)$: Intercepts at $x=2, x=-1$ (does not match)
• $f(x)=(x+2)(x-1)$: Degree 2 (not cubic, graph is cubic)
• $f(x)=(x+2)^2(x-1)$: Intercepts at $x=-2$ (multiplicity 2, touches) and $x=1$ (multiplicity 1, crosses), degree 3 (cubic, matches graph shape)
• $f(x)=(x+2)(x+4)(x-1)$: Intercepts at $x=-2, x=-4, x=1$ (extra intercept, does not match)

Answer:

C. $f(x)=(x+2)^2(x-1)$