Finding the equation of the parabola

**Chipset3600** · September 29th 2012, 11:37 AM

Hello guys, please help me, knowing that the parabola passes through the points A(0,1), B(-1,-2) e C(-2,7). How can i find the equation?

**johnsomeone** · September 29th 2012, 11:42 AM

The equation for a parabola would be knowing the values of $a, b, c$ in $y = ax^2 + bx + c$ .

What does C = (-2,7) on the parabola tell you? It says that when x = -2, the y value of that formula will be 7.

Thus $(7) = a(-2)^2 + b(-2) + c = 4a - 2b + c$ .

So C on the parabola tells you that $4a - 2b + c = 7$ .

A and B on the parabola will likewise tell you something. And if you know what a, b, and c are, then you have "found the parabola".

**MarkFL** · September 29th 2012, 11:46 AM

Let:

$y(x)=ax^2+bx+c$

From the given points, this gives the 3X3 linear system:

$a(0)^2+b(0)+c=1$

$a(-1)^2+b(-1)+c=-2$

$a(-2)^2+b(-2)+c=7$

Simplified:

$c=1$ this allows us to reduce the problem to the following 2X2 system

$a-b=-3$

$4a-2b=6$

Solve this system, and you will have the values of the coefficients $a,b,c$ which will give you the parabola you want.