SAT Question e1f9000d: Nonlinear Functions answer and explanation with Desmos solution

Choice B is correct. It's given that the function $h$ estimates that the object is $3,364$ feet above the ground when it's dropped at $t=0$. Substituting $3,364$ for $h\left(t\right)$ and $0$ for $t$ in the function $h$ yields $3,364=-16{\left(0\right)}^2+b$, or $3,364=b$. Substituting $3,364$ for $b$ in the function $h$ yields $h\left(t\right)=-16t^2+3,364$. When the object hits the ground, its height will be $0$ feet above the ground. Substituting $0$ for $h\left(t\right)$ in $h\left(t\right)=-16t^2+3,364$ yields $0=-16t^2+3,364$. Adding $16t^2$ to each side of this equation yields $16t^2=3,364$. Dividing each side of this equation by $16$ yields $t^2=210.25$. Since the object will hit the ground at a positive number of seconds after it's dropped, the value of $t$ can be found by taking the positive square root of each side of this equation, which yields $t=14.50$. It follows that the function estimates the object will hit the ground approximately $14.50$ seconds after being dropped.