Question

Which of the following options describes a parabola that is vertically compressed, opens downward, moved six units up, and moved two units to the left?

A) y = -2(x + 2)^2 + 6
B) y = -2(x - 2)^2 + 6
C) y = 2(x + 2)^2 + 6
D) y = 2(x - 2)^2 + 6

Answer 1

The equation that describes a vertically compressed, downward-opening parabola moved six units up and two units to the left is y = -2(x + 2)^2 + 6 (option A). The correct answer is A) y = -2(x + 2)^2 + 6.

Step-by-step explanation:

The equation that describes a vertically compressed, downward-opening parabola moved six units up and two units to the left is y = -2(x + 2)^2 + 6 (option A).

To understand this, let's break it down:

The negative sign in front of the 2 indicates that the parabola opens downward.

The (x + 2) term indicates that the parabola is moved two units to the left.

The (x + 2)^2 term represents the horizontally compressed parabola.

The +6 at the end indicates that the parabola is moved six units up.

Therefore, the correct answer is A) y = -2(x + 2)^2 + 6.