Question Suppose a parabola has a vertex (6, -6) and also passes through the point (8, -14). Write the equation of the parabola in vertex form.(1 point) show all your work

1 answer

The general equation of a parabola in vertex form is y = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex.

We are given that the vertex is (6, -6). So, h = 6 and k = -6.

We also know that the parabola passes through the point (8, -14). Plugging in these values into the equation, we get:

-14 = a(8-6)^2 + (-6)

Simplifying the equation further:

-14 = a(2)^2 - 6

-14 = 4a - 6

Rearranging the equation to solve for a:

4a = -14 + 6

4a = -8

a = -8/4

a = -2

Now that we have the value of a, we can write the equation of the parabola in vertex form:

y = -2(x-6)^2 - 6

Therefore, the equation of the parabola in vertex form is y = -2(x-6)^2 - 6.