Question 885280
Starting in standard form might be easier.


{{{y=a(x-h)^2+k}}}, instructive model for standard form
{{{y=a(x-1)^2-1}}}, more specific equation but without yet knowing a=whatStillUnknown
{{{7=a(3-1)^2-1}}}, allowing to find a solution for a.


{{{7=a2^2-1}}}
{{{7=4a-1}}}
{{{4a=7+1}}}
{{{4a=8}}}
{{{a=2}}}
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The function still in standard form is {{{highlight(f(x)=2(x-1)^2-1)}}}.
You can simplify into general form if that is what you want.