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I already know the values $x, c$ and $y$ in this equation: $y = ax^2 + bx + c$

I would like to know one or more methods for finding the values of a and b.

  • 0
    what are the values? – 2017-02-28
  • 0
    This is a set of values, not a single pair. Fix $b$ and then you can derive $a$ as a function of $b$ – 2017-02-28
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    You are not able to find a unique $(a,b)$ if one point is given however if there are two points given then you can form simultaneous equations and solve a and b. – 2017-02-28

1 Answers 1

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Substituting the known values you find an eqaution in the two unknown $a,b$ that,if $x\ne 0$,has infintely many solutions of the form: $$ a=\frac{y-bx-c}{x^2} $$

if $x=0$ than the equation is an identity if $y=c$ and has no solutions in $y \ne c$.