A parabola opening up or down has vertex (0, - 1) and passes through (6,

-

10). Write its equation in vertex form.

y + 1 = (11/36) (x - 0) ^2

Step-by-step explanation:

Suppose that the parabola opens UP. We adapt the equation

y - k = a (x - h) ^2 as follows: k = 0 because the vertex is at (0, - 1); also h = 1.

Then we have:

y + 1 = a (x - 0) ^2

We are told that (6, 10) is on the parabola. Subtracting 6 for x and 10 for y, we get:

10 + 1 = a (6 - 0) ^2, or 11 = a (6^2)

Then 11/36 = a

The equation of the parabola in vertex form is y + 1 = (11/36) (x - 0) ^2