SOLUTION: write an equation in standard form of the parabola that has the same shape as the graph of {{{f(x)=-7x^2}}}, but which has a maximum of {{{9}}} at {{{x=3}}}.

First let's draw the graph of the first equation:



Notice that since its vertex is  it has a maximum
of  at .  Now let's plot the point .



We now need to shift the graph of  so that its
vertex  shifts to the point  and the second shifted function .

We first shift the graph horizontally 3 units to the right.
This is done by replacing  in the right side of  by 
, getting . 



But now that graph must be shifted vertically upward by  units.
This is done by adding  to the right side of ,
getting .  Now we draw that graph, and get



So the answer is }.  Notice that it has the
same shape as the original graph of .

Edwin