Finding a Parabola using three points, no equations

[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 don't remember what the points were, so let's just say they were (-1, 0), (3,2), (4,1)

How would you find the two equations?

 

[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.)

 

[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!