Question

Suppose a parabola has an axis of symmetry at x = –7, a maximum height of 4, and also passes through the point (–6, 0). Write the equation of the parabola in vertex form.

Answer 1

@Ashleyisakitty

Answer 2

Working on this. But, to help you get started:\[y=a(x-h)^{2}+k\] is the "vertex form" of a parabola.

Hint #2: The vertex AND the point at which the parabola achieves its max height are embodied in the problem statement. You can find the point that represents the max height, as well as draw quite a bit of the parabola.

Hint #3: Does the graph of this parab. open up or down? How do you know that?

Answer 3

What is the value of a, and why?

Answer 4

is that what i am trying t find?? because h=-4 and k=4 but i have no clue what a equals :P

Answer 5

k=4 is great. Mind explaining how y ou obtained h=-4? Hint: What does "axis of symmetry" mean?

Answer 6

just 4 sorry :P and it is the height. :)

Answer 7

-7 h=-7

Answer 8

Great!

Answer 9

ok.. currently i have \[y=a(x-7)^{2}+4\] right??

Answer 10

Substitute what you already have into \[y=a(x-h)^{2}+k\] and then determine what else you still have to find.

Answer 11

Looks good. Why not go ahead and solve for a? you can always test your equation by substituting the point (-6,0) and verifying that the resulting equation is true.

Answer 12

ok so it would be
\[0=a(-6-7)^{2}+4\]
the just solve for a??

Answer 13

By the way, that exponent, 2, must go outside the parentheses: a(-6-7)^2.

Answer 14

And, Mel, that should really be -6+7, not -6-7. I'm going to ask you to figure out why and to correct your equation.

Answer 15

and thanks for using the equation editor. So much clearer!!

Answer 16

i lied false.. i should have\[-4=a(1)^{2}\]

Answer 17

so a=-4??? :)

Answer 18

One thing at a time:
1. Inside those parentheses you should have x-h. In this problem, what is h? (You were correct earlier.)
2. We don't really want to multiply -6+7 by a, do you? Think about this and see if you can figure out better wording.
3. Your value for a is perfectly right.

Answer 19

yay!! thank you sooo much!!! :D

Answer 20

My great pleasure. Post some more questions when you're ready!

Answer 21

trust me i will be!! i am horrible at math =-P