type the correct answer in each box. use numerals instead of words. what is the equation of the quadratic…

Explanation:

Step1: Recall vertex - form of quadratic function

The vertex - form of a quadratic function is $f(x)=a(x - h)^2 + k$, where $(h,k)$ is the vertex of the parabola. Since the function has a minimum at $(7,-3)$, then $h = 7$ and $k=-3$. So the function is $f(x)=a(x - 7)^2-3$.

Step2: Find the value of $a$

The function passes through the point $(9,9)$. Substitute $x = 9$ and $y = 9$ into the equation $f(x)=a(x - 7)^2-3$. We get $9=a(9 - 7)^2-3$. First, simplify the right - hand side: $9=a(2)^2-3$, which is $9 = 4a-3$. Add 3 to both sides: $9 + 3=4a$, so $12 = 4a$. Divide both sides by 4, we find $a = 3$.

Answer:

$f(x)=3(x - 7)^2-3$ So the blanks should be filled with 3, 7, - 3 respectively.