Question

Write the equation in vertex form of the parabola with the vertex (-4,-4) that goes through the point (-2,-16)

Answer 1

`- 3(x + 4) {}^(2) - 4`

Explanation:

Vertex form is

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

We know that h and k are both -4. Let x be -2 and y be -16.

`a( - 2 + 4) {}^(2) - 4 = - 16`

`a(2) {}^(2) - 4 = - 16`

`4a - 4 = - 16`

`4a = - 12`

`a = - 3`

So the equation in vertex form is

`- 3(x + 4) {}^(2) - 4`