SAT Question ef926848: Nonlinear Functions answer and explanation with Desmos solution

Choice A is correct. Let $x$ represent the side length, in inches, of square P. It follows that the perimeter of square P is $4x$ inches. It's given that square Q has a perimeter that is $176$ inches greater than the perimeter of square P. Thus, the perimeter of square Q is $176$ inches greater than $4x$ inches, or $4x+176$ inches. Since the perimeter of a square is $4$ times the side length of the square, each side length of Q is $\frac{4x+176}{4}$, or $x+44$ inches. Since the area of a square is calculated by multiplying the length of two sides, the area of square Q is $\left(x+44\right)\left(x+44\right)$, or ${\left(x+44\right)}^2$ square inches. It follows that function $f$ is defined by $f\left(x\right)={\left(x+44\right)}^2$.