# Thread: Writing the equation for parabolas

1. ## Writing the equation for parabolas

I need to write the equation for a parabola that passes through the points (0,4),(-3,1) and has an axis of symmetry at x=-2

2. Originally Posted by Vuong
I need to write the equation for a parabola that passes through the points (0,4),(-3,1) and has an axis of symmetry at x=-2
use the form ...

$y = a(x-h)^2 + k$

note that $h$ = x-value of the vertex

3. Originally Posted by skeeter
use the form ...

$y = a(x-h)^2 + k$

note that $h$ = x-value of the vertex
What is a h and k?

4. $h$ is the horizontal translation and k is the vertical translation

as the axis of symmetry is $x = -2$ then $h = -2$

I.e $y = a(x-(-2))^2 + k$

5. Originally Posted by Vuong
What is a h and k?
That's what you are to find- don't expect people to do the whole problem for you, you won't learn that way. skeeter did just tell you what h is: "h= x-value of vertex". You don't know what k (the y value of the vertex) is but you do h: "the parabola has an axis of symmetry at x= -2". Put in that value for h and you have an equation in a and k. Use the fact that (0,4) and (-3,1) are on the parabola, and so satisfy the equation, to get two equations to solve for a and k.