# Find Equation for the Parabola- Help, Please?

1. May 12, 2004

### dmbeluke

Each pair of the following three lines cross at a point. Those points are the y-intercept, one of the x-intercepts, and the vertex of a parabola. Can you please explain to me how to find an equation for the parabola? And the other x- intercept?

y+8x=32
y+5x=32
y+3x=12

I have been trying everything I can think of. I think they cross at 0. And I know the equation has to be squared, but I'm so lost on this one, I don't know what else to do. Any advice would be appriciated. Thank you.

2. May 13, 2004

### arildno

Step 1:
Determine the 3 pairs of (x,y)-values that solves the 3 pairwise systems of linear equations.
Let's call these:
$${r}_{1}=(x_{1},y_{1}), {r}_{2}=(x_{2},y_{2}), {r}_{3}=(x_{3},y_{3})$$

Step 2.
The general equation for a parabola when the y-coordinate is a function of the x-coordinate is:
$$y=ax^{2}+bx+c$$, where a, b,c are constants.

You do know something of the parabola you're after, namely that the 3 pairs $$r_{1},r_{2},r_{3}$$ are on it.
How can this information be used in order to determine a,b,c?