# How to solve for a & b in a parabolic equation?

Not a mathematician at all here, actually a programmer and this came up... I need some help on something that is pretty basic I'm guessing. Given the following formula how would I go about solving the scenarios?

given the formula: y = ax^2 + bx + c

if I know that x = 20 and c = 100, how would one go about solving for y, a, and b.

I know this has something to do with the quadratic formula, but again, I really I'm not a math person at all and don't know where to begin. I do understand basic linear algebra but that's about it.

• You simply can't get a solution that's unique, You have 1 equation and 3 variables Commented Mar 6, 2016 at 20:41

## 1 Answer

You have one equation containing (originally) 5 symbols of unknown value: x, y, a, b, c. Then you're given the values of x and c.

The revised equation is: $y = 400a + 20b + 100$

This is a single linear equation containing three unknowns. This is not enough to know the values of a, b and y, but it does give you a relationship between them which could be represented as a plane surface in three dimensional space.

If someone gave you the values of a and b it would be easy to calculate the value of y.