Question

Can you use algebra to find a quadratic equation if your know the coordinates of just ONE point on its graph?

Can you use algebra to find a quadratic equation if your know the coordinates of just TWO points on its graph?
If so, what information is needed?

Answer 1

You mus know 3 coordinats if you want find a quadratic equation.

Answer 2

In general, you need three points, but if you know that one of the points is the vertex, then that gives you extra information. If you know (h,k), then the parabola is

y-k = a(x-h)^2

so only "a" is unknown. The second point will provide that.