First, let's look at the vertex form of the quadratic equation:
[tex]y=a(x-h)^2+k[/tex]Where the vertex is located at (h, k).
The vertex is the point of maximum or minimum of the quadratic function.
So if the minimum is at (7, -3), we have h = 7 and k = -3.
Then, to find the value of a, let's use the point (9, 9) in the function:
[tex]\begin{gathered} y=a(x-7)^2-3\\ \\ 9=a(9-7)^2-3\\ \\ 9=4a-3\\ \\ 4a=12\\ \\ a=3 \end{gathered}[/tex]Therefore the function is f(x) = 3(x - 7)² - 3.
