How do you find the quadratic coefficient a, b, and c, given some values of x and y?

For example: Suppose we have f(0.1524)=0.9961 f(0.8258)=0.0782 f(0.5383)=0.4427 and given the quadratic equation: $$y = ax^2 + bx + c$$, then can you find values of x and y?

Is there a formula to find these a, b, and c? when I think about the general formula, but in this case y=0. So, it does't work. When I think about substitute by the formula: $$y = ax^2 + bx + c$$, I cannot get go long; because we have three unknown in one equation. So, what you suggest as next step.

Thank you!

• You get three linear equations for three unknowns. – H. Gutsche Jan 17 '19 at 15:47
• Just solve a system of equations for $a$, $b$, and $c$ by plugging in $x$ and $y$ in the equation $y = ax^2+bx+c$. – KM101 Jan 17 '19 at 15:47
• Thank you both H.Gutsche and KM101. It is very clear now. – user777 Jan 17 '19 at 15:57

If you are given $$3$$ points with distinct $$x$$ values, by substituting those values inside $$y=ax^2+bx+c$$, we can obtain $$3$$ linear equations in terms of $$a, b$$, and $$c$$.