Question

Use the image to answer the question.

A parabola is drawn on a coordinate plane. Both axes range from negative 5 to 5 in one-unit increments.
▼Click for Long Desc
The parabola descends and then rises in quadrant 2. The curve passes through left parenthesis negative 3.6 comma 5 right parenthesis, left parenthesis negative 3 comma 2 right parenthesis, has a valley at left parenthesis negative 2 comma 0 right parenthesis, rises through left parenthesis negative 1 comma 2 right parenthesis, and left parenthesis negative 0.4 comma 5 right parenthesis. All values are approximate.

The graph shows the starting function y=2(x+2)2
. The graph of which of the following functions is a reflection of the starting function about the origin?

(1 point)

y=2(−x+2)2


y=−2(−x+2)2


y=2(x+2)2


y=−2(x+2)2

Answer 1

Reflection about the origin sends y = f(x) to y = -f(-x). For f(x) = 2(x+2)^2 this gives

y = -2((-x)+2)^2 = -2(−x+2)^2

(also equal to y = -2(x-2)^2).

So the correct choice is y = −2(−x+2)^2.