How do I find the "A" quanity in the vertex form of a parabola?

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The vertex form of a parabola is `y=a(x-h)^2+k` where the vertex is (h,k).

If you know the vertex you will need to know one more point to find a.

For example, suppose you are given a parabola with vertex at (3,4) going through the point (2,6). (Sometimes you are given the additional point; you might have to read it off of the graph. Or perhaps you will be told about an intercept.)

Then you know `y=a(x-3)^2+4` . To find a substitute the x and y values of the other known point. Here x=2 and y=6:

`6=a(2-3)^2+4`

`6=a+4 ==> a=2` so the function was `y=2(x-3)^2+4` .

Thank you!

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