Question

Which equation represents a parabola with the same vertex as y = -1/2(x + 3)^2 - 7 but that opens in the opposite direction?

A) y = 1/2(x + 3)^2 - 7
B) y = -1/2(x - 3)^2 - 7
C) y = -1/2(x + 3)^2 + 7
D) y = -1/2(x + 3)^2 - 3

Answer 1

The equation that represents a parabola with the same vertex but opens in the opposite direction is y = 1/2(x + 3)^2 - 7 (option A).

Step-by-step explanation:

The equation that represents a parabola with the same vertex as y = -1/2(x + 3)^2 - 7 but opens in the opposite direction is y = 1/2(x + 3)^2 - 7 (option A).

To determine the equation that opens in the opposite direction, we need to change the coefficient of the x-squared term to its opposite sign while keeping the vertex the same. In this case, the original equation has a coefficient of -1/2, so the opposite sign is 1/2.

By changing the coefficient to 1/2, we get a parabola that opens upwards instead of downwards.