Question

Can some one please explain how to write the equation of a parabola in vertex form?
Axis of symmetry : x = -7
max height of 4
and also passes through the point (-6,0)

Answer 1

Please don't just give the answer. I really need to know how.

Answer 2

Axis of symetry = x value of vertex (= h)
max/min height = y value of vertex (= k)

Now you have the equation:
\[y = a(x-h)^2 + k\]

We know h and k, to find a, plug in the given values of x and y (the point on the parabola)

Answer 3

Okay, please don't go, I'm going to try it.

Answer 4

A = 4?

Answer 5

@DDCamp

Answer 6

Would the equation be y = 4 (x + 6)^2 + 0 ??

Answer 7

We know h=-7, and k=4 (from the axis of symmetry and the max height)
We know that the point (-6,0) is on the graph (x = -6 when y=0)
\[y = a(x+7)^2+4 \\ 0 = a(-6+7)^2 + 4\]

Answer 8

Oh, I did them the other way. so a = -4?

Answer 9

And the equation would be y = -4(x + 7)^2 + 4 ??

Answer 10

Yup

Answer 11

Is that the final equation/answer? there's no factoring or anything of the nature?

Answer 12

Nope. That's in vertex form.

Answer 13

Thank you so much! @DDCamp