PLEASE HELP ME
The graph of f(x) = −x2 − 2x + 8 is shown. Which of the following describes all solutions for f(x)?

a parabola passing through negative 4 comma zero, negative 1 comma 9, zero comma 8, and 2 comma zero

A. (x, −x2 − 2x + 8) for all real numbers

B. (−4, 0), (−1, 9), (0, 8), (2, 0)

C. (−4, 0), (2, 0)

D. (x, y) for all real numbers

This is a bad question.  It should really be asking about the solutions of f(x)=0 (an actual equation) or the zeros of f(x).

The zeros of a function f(x) are the xs where f(x)=0.  That means where the curve intersects the x axis.  That's (-4,0) and (2,0) on the graph.

C   (-4,0), (2,0)

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.