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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

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  1. anonymous
    • 5 years ago
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    You only have three points, so you'll end up with an infinite number of parabolas. Were you only given two points?

  2. anonymous
    • 5 years ago
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    Two points, I meant to say.

  3. anonymous
    • 5 years ago
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    Yes, so i guess i need to find the vertex, which would then give me 3 points right?

  4. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    Okay thanks!

  8. anonymous
    • 5 years ago
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    No probs. Just check those equations. I did them on-the-fly.

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