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The vertex form is a(x-h)2 +k=y

We know that (h,k) is the vertex and in this problem h=3 and -2 =k

So we have

a(x-3)2 -2=y

Now to fine a, we simply need one more point, but we have that.

Plug in (4,3)

a(4-3)2 -2=3

or a(4-3)2 =5

a(1)=5 so a=5.

the coefficient is 5.

Check it:

5(4-3)2 -2=3

5(1)-2=3 as desired.

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