Answer
$y = 2\sqrt {3(x-2)-{(x-2)}^{2}}$
Work Step by Step
We first see that our new graph is our old one shifted to the right by $2$ units because the initial graph has the zeros $0$ and $3$ and the new one has the zeros of $0 +2$ and $3 + 2$ which is $2$ and $5$. Therefore we subtract $2$ from the $x$ within $f(x)$ giving us:
$y = \sqrt {3(x-2)-{(x-2)}^{2}}$
We then see that instead of having $y=1.5$ as the max in our function, our new function reaches $y = 3$. Since we know that $3 = 2(1.5)$, we know that our new graph is vertically stretched by 2. Therefore we must multiply our entire function by 2 giving us:
$y = 2\sqrt {3(x-2)-{(x-2)}^{2}}$ as our final answer for the function of our new graph.
