Question

Question #ea797

Answer 1

The vertex form of the equation of a vertically oriented parabola is:
`y = a(x - h)^2 + k` where a is the coefficient of the `x^2` term and `(h,k)` is the vertex

Explanation:

Given: `y = -2x^2 - 16x -32`

Please observe that `a = -2`

Add zero to the right side of the equation in form of `ah^2 - ah^2`:

`y = -2x^2 - 16x + -2h^2 - -2h^2 -32`

Factor -2 out of the first three terms on the right:

`y = -2(x^2 + 8x + h^2) + 2h^2 -32`

Using the pattern `(x - h)^2 = x^2 - 2hx + h^2`, we set the middle term in the right side of the pattern equal to middle term in the equation:

`-2hx = 8x`

`h = -4`

Substitute the left side of the pattern into the equation:

`y = -2(x - h)^2 + 2h^2 -32`

Substitute - 4 for h:

`y = -2(x - -4)^2 + 2(-4)^2 -32`

Combine the constant terms:

`y = -2(x - -4)^2`

This is the vertex form.