Question

Enter the equation of the parabola in vertex form that has its vertex at (4,–13) and passes through the point (6,–5).

Answer 1

Explanation:

If you plot the vertex and the point that it goes through, the point it goes through is above the vertex, so the vertex is a positive one that opens upwards. The general vertex form of a parabola of this type is

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

We have the x, y, h, and k. We will plug all those in and solve for a. That looks like this:

`-5=a(6-4)^2-13` which simplifies to

-5 = 4a - 13 and

8 = 4a so

a = 2

That means that the paraobola in vertex form is

`y=2(x-4)^2-13`