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

1. anonymous

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

2. anonymous

Two points, I meant to say.

3. anonymous

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

4. anonymous

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).

5. anonymous

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

6. anonymous

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.

7. anonymous

Okay thanks!

8. anonymous

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