SOLUTION: How do I find the missing A value in a quadratic equation?

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Question 760085: How do I find the missing A value in a quadratic equation?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I'm hoping this answers your question.
ax%5E2%2Bbx%2Bc=0 is one of infinite equivalent equations, and you may not need to find a.
If you know that the solutions of a quadratic equation are x=c and x=d, you can conclude that one of the equivalent equations with those solutions is
%28x-c%29%28x-d%29=0 which can also be written as x%5E2-%28c%2Bd%29x%2Bcd=0
If you multiply both sides of the equal sign times a non-zero number, you get an equivalent equation, such as
2x%5E2-2%28c%2Bd%29x%2B2cd=0 if you multiply times 2, or
ax%5E2-a%28c%2Bd%29x%2Bacd=0 if you multiply times a number a such that a%3C%3E0.

On the other hand, If you are looking for a quadratic function
y=ax%5E2%2Bbx%2Bc, you need at least 3 (x,y) points (or equivalent information) to find a, b, and c.
The coordinates of the vertex and one other point would do too.