Vertex question (1 Viewer)

[Galapagos]

I'm currently doing revision and I came across a set of questions I have no memory of learning. I've been trying to work it out for the past 2 hours but the more I stare at it, the more I get confused.

K, so the type of question is this: you have to work out the equation of a parabola; you're given a set of points, such as the x-intercepts e.g. (3,0),(-2,0), and the vertex e.g. (7,9)...so how do you do it?

I know how to do it with both x-intercept(s) and y-intercept(s), but with this type of q. my brain just stalls. I'm sure it's obvious, but it's really bugging the shit out of me. Any help would be appreciated!

 

[Galapagos]

Anyone?

 

[Carrotsticks]

Suppose I had the two X intercepts:

(-2,0) and (4,0)

I can deduce that the parabola has the general form:



For some constant K.

Then I would sub the 3rd point (could be the vertex, but any point will do) to find the value of k, hence yielding the parabola's equation.

Every parabola is unique to a set of 3 points.

That is: If you give me 3 random points on a plane, I can draw ONLY 1 unique parabola passing through all 3 points.

This is because if you look at the general equation of the parabola, it is:



So to solve for A, B and C, you will need 3 points to sub in (the proof for this and for the general N'th degree polynomial is far more complex, but not necessary here)

 

[Galapagos]

Thank you! Couldn't find that anywhere in any of my gazzilion textbooks.
Would rep if I could.