Let's put more details in the given graph,
We will generate the equation of the graph based on the following form:
[tex]\text{ f(x) = a(x - h)}^2\text{ + k}[/tex]
We get,
[tex]\text{ f(x) = a(x - h)}^2\text{ + k}[/tex][tex]\text{ f(x) = a(x - 1)}^2\text{ + }(-9)[/tex][tex]\text{ f(x) = a(x - 1)}^2\text{ }-9[/tex]
Let's find a, use f(-2) = 0.
[tex]f\mleft(-2\mright)=0[/tex][tex]\text{ 0 = a\lbrack(-2) - 1\rbrack}^2\text{ - 9}[/tex][tex]\text{ 0 = a(-2 - 1)}^2\text{ - 9}[/tex][tex]\text{ 0 + 9 = a(-3)}^2\text{ - 9 + 9}[/tex][tex]\text{ 9 = 9a}[/tex][tex]\text{ }\frac{\text{9}}{9}\text{ = }\frac{\text{9a}}{9}[/tex][tex]\text{ a = 1}[/tex]
Let's now complete the equation.
[tex]\text{ f(x) = a(x - 1)}^2\text{ }-9[/tex][tex]\text{ f(x) = (1)(x - 1)}^2\text{ }-9\text{ = (x - 1)}^2\text{ }-9\text{ }[/tex][tex]\text{ f(x) = x}^2\text{ - 2x + 1 - 9}[/tex][tex]\text{ f(x) = x}^2\text{ - 2x - 8}[/tex]
Therefore, the answer is letter A.
