# Finding a Parabola using three points, no equations

1. Mar 10, 2008

### DarlingAly

Can someone help me with this problem? I already turned it in, knowing it was wrong, and now I want to know how to do it.

they gave me three points and no equations and expected me to find the standard form and vertex form of the parabola. i dont remember what the points were, so lets just say they were (-1, 0), (3,2), (4,1)

How would you find the two equations?

2. Mar 10, 2008

### HallsofIvy

First, it helps to know what the "standard form" and "vertex form" for a parabola are! The "standard form" for a parabola (with vertical axis of symmetry) is y= ax2+ bx+ c and the "vertex form" is y= a(x- x0)+ y0. For the first, you need to find a, b, and c. For the second, you need to find a, x0, and y0.

In either case use the points you are given to replace x and y in the equation: saying that (-1, 0) is a point on the parabola means that x= -1, y= 0 satify the equation:
0= a(-1)2+ b(-1)+ c. For (3, 2), 2= a(3)2+ b(3)+ c, and for (4, 1), 1= a(4)2+ b(4)+ c. That gives you 3 equations to solve for a, b, and c.

You can do exactly the same thing with the vertex form to find a, x0, and y0.

(If the axis of symmetry is not vertical, 3 points are not enough to determine the equation.)

3. Mar 10, 2008

### DarlingAly

Yeah I knew the standard form and the vertex form. I also knew the equations. It's just that I kept getting fractions while everyone else got the vertex to be a (3, -5) with the numbers i can't remember.. haha

I just wanted to know if anyone did it different.
Thanks!