Question

A parabola has a vertex (-3, -2) and contains the point (-5, 6). Write the equation for this parabola in vertex form.

Answer 1

`y = 2(x +3)^2 -2`

Explanation:

Given

`(h,k) = (-3,-2)` --- vertex

`(x,y) = (-5,6)` --- point

Required

Determine the equation

The general form is:

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

First, we solve for a:

Substitute
`(h,k) = (-3,-2)` and
`(x,y) = (-5,6)` in
`y = a(x - h)^2 + k`

`6 = a(-5 - (-3))^2 - 2`

`6 = a(-2)^2 - 2`

`6 = 4a - 2`

Solve for a

`4a = 6 + 2`

`4a = 8`

`a = 2`

So:

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

`y = 2(x - (-3))^2 -2`

`y = 2(x +3)^2 -2`