How to find equation of a parabola given 3 points? (1 Viewer)

[usels]

Hi,

Given 3 points, say (-a,0), (0,h), and (a,0) how do you find the equation of the parabola?

thx

 

[Xayma]

Those three points are remarkably easy to find it with.

The x intercepts are x=a and x=-a

The y intercept is y=h.

By symmetry of a parabola the vertex is at h.

So we get:

y=-x² + h
where a²=h if h>0
and a≠0

y=x² + h
if where a²=h, if h<0.

I think...

 

[ngai]

few ways:
1) it is y=-kx^2 + h
then sub in a,0 and find k
2) it is y=-k(x-a)(x+a)
then sub in 0,h and find k
3) it is y=px^2+qx+r
sub in (a,0), (-a,0), (0,h) to find p,q,r by simultaneous eqns

 

[Slidey]

I know this is a tangent, but if you have three points and given f(x)=ax^2+bx+c, could you not set up three simultaneous equations and solve?

EDIT: Sorry. Didn't see ngai's post.