Question

question 5 of 10
which of the following polynomial functions is graphed below?
a. $f(x) = (x + 2)(x - 3)^2(x + 4)$
b. $f(x) = (x - 5)(x - 1)^2(x - 1)$
c. $f(x) = (x - 2)^2(x - 3)(x - 4)$
d. $f(x) = (x - 5)(x - 1)^2(x + 1)$

Explanation:

Step1: Identify x-intercepts

The graph crosses/touches x-axis near x=-4, x=-2, x=3.

Step2: Check intercepts in options

Option A has roots x=-4, x=-2, x=3 (double root at 3, matching touch).

Step3: Verify double root behavior

Double root at x=3 means graph touches x-axis there, consistent with option A.

Answer:

A. $f(x)=(x + 2)(x - 3)^2(x + 4)$