Question

There's an equilateral triangle with three vertices.
find the equation of the parabola that passes through the three points. How do I solve this?

Answer 1

Hmm....Let's first make up some sides for this hypothetical triangle.

0, 3 3,0 -3,0

I'm using the same ones off of another website that asked the same question so you can reference it if my answer doesnt make enough sense to you. :)

You first will want to put it in vertex form. You can only do this once you've established that it passes through the parabola. FYI, the vertex is 0,3.

Check this out for finding the vertex: http://www.uiowa.edu/~examserv/mathmatters/tutorial_quiz/geometry/findingvertexofparabola.html

Go ahead and plug in one of your points.
0 = a(3)^2 + 3

From here, it's just simplifying. :)
-3 = 9a
a = -3/9
= -1/3

And now you're all done!

y = -1/3 x^2 + 3

If this still doesn't make sense to you, I can throw you a couple of sites that might make it easier for you. :)

Answer 2

I think I get it thank you