Question

The vertex of this parabola is at (3,-2). Which of the following could be itsequation?6-5(-3,-2)55A. y = -2(x - 3)2 - 2B. y = -2(x + 3)2 + 2C. y = -2(x - 3)2 + 2O D. y = -2(x + 3)2 - 2

Answer 1

Given:

The vertex of a parabola is (-3,2).

The objective is to choose the correct equation of the parabola.

The general equation of parabola is,

`y=a(x-h)^2_{}+k`

Here, (h,k) represents the vertex of the parabola, a represents the rate of the curve in upward or downward.

Since, the curve is moved 2 units in downward direction, a = -2 and it is given that (h,k) = (-3,2).

On plugging the values in the general equation,

`\begin{gathered} y=-2(x-(-3))^2+2 \\ y=-2(x+3)^2+2 \end{gathered}`

Henc.