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

Answer:

Step-by-step 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

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