Question

What is the quadratic equation that goes through the points (-8,0) and (4,5) to find the a,b,c of the parabola

Answer 1

You only have three points, so you'll end up with an infinite number of parabolas. Were you only given two points?

Answer 2

Two points, I meant to say.

Answer 3

Yes, so i guess i need to find the vertex, which would then give me 3 points right?

Answer 4

Well, two points won't be enough.

You have two linear equations given your points:
\[64a-8b+c=0\]and\[16a+4b+c=5\]
You need three linearly independent equations for a unique solution (a, b, c).

Answer 5

So can the just be a quadratic equation with 2 points? Or to do anything with this problem would I need 3 points?

Answer 6

You can get *something* out of it, though you won't get something unique. You'll get an infinite number of possibilities.
You can solve those two equations to get\[b=4a+\frac{5}{12}\]and then sub. that back to find \[c=\frac{10}{3}-32a\]but this will be as far as you can get. You now have the choice of any 'a' you wish, and the equations for b and c will give you a quadratic that will contain your points.

Answer 7

Okay thanks!

Answer 8

No probs. Just check those equations. I did them on-the-fly.