SAT Question cb29c54c: Nonlinear Functions answer and explanation with Desmos solution

Choice B is correct. The vertex of the graph of a quadratic equation is where it reaches its minimum or maximum value. When a quadratic equation is written in the form $y=a(x-h{)}^2+k$, the vertex of the parabola represented by the equation is $(x,y)=(h,k)$. In the given equation $y=-16(x-5.6{)}^2+502$, the value of $h$ is $5.6$ and the value of $k$ is $502$. It follows that the vertex of the graph of this equation in the xy-plane is $(x,y)=(5.6,502)$. Additionally, since $a=-16$ in the given equation, the graph of the quadratic equation opens down, and the vertex represents a maximum. It's given that the value of $y$ represents the estimated height, in feet, of the toy rocket $x$ seconds after it is launched into the air. Therefore, this toy rocket reaches an estimated maximum height of $502$ feet $5.6$ seconds after it is launched into the air.