Given information:

The given function is \(f(x)=x^2\).

Concept Used:

If a is positve real number, then the graph of \(f(x-a)\) is the graph of \(y=f(x)\) shifted to the right a units.

If \(a>1\), the graph of \(y=cf(x)\) is the graph of \(y =f(x)\) stretched vertically by a.

If a is positve real number, then the graph of \(f(x)-a\) is the graph of \(y=f(x)\) shifted downward a units.

Calculation:

First, we have to shift the graph to the right by 7 units.

\(f(x-7)=(x-7)^2\)

Now, stretched the graph by a factor of 9 units.

\(9f(x-7)=9(x-7)^2\)

Now, shift the above graph downward by 3 units.

\(9f(x-7)-3=9(x-7)^2-3\)

Compare the new equation with the equation \(y=a(x-h)^2+k\), we get

\(h=7\) and \(k=-3\)

Final Statement:

The new coordinates of the vertex for the new parabola function is (7,-3)

The new function is

\(g(x)=9(x-70^2-3)\)