SAT Question 39714777: Nonlinear Functions answer and explanation with Desmos solution

Choice B is correct. For a quadratic function defined by an equation of the form $p\left(x\right)=a{\left(x-h\right)}^2+k$, where $a$, $h$, and $k$ are constants and $a>0$, the minimum value of the function is $k$. Subtracting $57$ from both sides of the given equation yields $p\left(x\right)=x^2-57$. This function is in the form $p\left(x\right)=a{\left(x-h\right)}^2+k$, where $a=1$, $h=0$, and $k=-57$. Therefore, the minimum value of the function $p$ is $-57$.