# General Solutions for three-point parabola

1. Apr 26, 2004

### Hyperreality

I'm having problems solving this particular question
Using matrix calculation to find a general solution for a parabola that passes through points (x1,y1), (x2, y2), (x3, y3).

First I setted my equations

ax1^2+bx2+c=y1

ax2^2+bx2+c=y2

ax3^2+bx2+c=y3

But I've no idea on how I should set up the augmented matrix. I presume the general solution is referring to the solving the constants a, b and c.

Any hints and suggestions is appreciated.

2. Apr 26, 2004

### arildno

First of all, your equations are incorrect.
In the first equation, the term "bx2" should read "bx1", while in your third equation the term "bx2" should read "bx3" (I assume these were typos..)

Look at the the left-hand side of your equations.
How can you rewrite this side as a matrix-vector product, where you know the entries in the matrix, while the vector is the unknown?