How can I determine a parabola given two points?

[dtl42]

If given two arbitrary points on a parabola, is there anyway to determine an explicit equation for that parabola. I know there are multiple possible parabolas, but how can I find just one of them?

 

[rock.freak667]

the general form of a parabola is $y=ax^2 +bx+c$

so given two points on the parabola, that would be insufficient to find a,b and c. If there is something else given about those 2 points then you may be able to find it.

 

[Gib Z]

If given two points, and you want the family of parabolas to go through them, just substitute those points into the general form of a parabola and you should get some simultaneous equations. You won't able able to get unique solutions for them, as you know, because there are many parabolas that go through those 2 points. If you want just any, choose any solution to the equations.