Quadratic graphs

I need to calculate an equation
ax^2 + bx + c
but all im given are datas such as the vertex and intercepts.
can it be done, or do i need more infos?

The 'turning' point is the point where dy/dx is 0, i.e. 2ax + b = 0.

The curve meets the y axis at the point x=0, so (0,c).

So given the minimum or maximum of the curve is (x,y) and the curve meets the y-axis at (0,z), you have:

z = a*0^2 + b*0 + c => z=c
2ax+b=0
ax^2+bx+c=y

2ax+b=0
bx=y-z-ax^2
=> b=((y-z)/x)-xa
b=-2xa
=> -xa=((y-z)/x)
=>

c=z
a=(z-y)/(x^2)
b=2(y-z)/x

>>1
use x-intercepts to get binomial factors, set equal to y
put a k in front of the expression, y = k(factor#1)(factor#2)
substitute any other point into your equation, putting its values in for x and y, solve for k
re-express equation as y = function of x.

>>3
that was more like what i was expecting, but some parabolas only intercept once

>>3
I'm sick of this "just get more ram!" bullshit. My 286 did almost as much functionality-wise as my current multi-ghz machine. Yeah, really. Sure, there was no multi-tasking, but I did the mostly the same things as I do today.
Hello, fuckers, just because you can eat ram doesn't mean you should. It costs money and also reduces the number of programs you can run.
I can see it now: in another ten years programs will have minimum footprint of 1GB, but they'll just do more of the same

>>4
that's alright, then factor #1 and #2 are the same thing twice.
if you have no x-intercepts at all, then you have imaginary values associated with them, revealed by the quadratic formula x = -b etc (google for it)