SAT Question 358f18bc: Nonlinear Functions answer and explanation with Desmos solution

The given function can be rewritten in the form $f\left(x\right)=a{\left(x-h\right)}^2+k$, where $a$ is a positive constant and the minimum value, $k$, of the function occurs when the value of $x$ is $h$. By completing the square, $f\left(x\right)=x^2-48x+2,304$ can be written as $f\left(x\right)=x^2-48x+{\left(\frac{48}{2}\right)}^2+2,304-{\left(\frac{48}{2}\right)}^2$, or $f\left(x\right)={\left(x-24\right)}^2+1,728$. This equation is in the form $f\left(x\right)=a{\left(x-h\right)}^2+k$, where $a=1$, $h=24$, and $k=1,728$. Therefore, the minimum value of the given function is $1,728$.