SAT Question c95686e9: Nonlinear Functions answer and explanation with Desmos solution

1$.It’sgiventhat$h ( t ) = - 16 t^{2} + b$estimatesaball’sheight,infeet,aboveafloor$t$secondsaftertheballisreleased,where$b$isaconstant.I{t}^{\prime }salsogiventhatthefunctionestimatesthattheballis＄19.36$ feet above the floor when it is released at $t=0$. Substituting ＄19.36$for$h ( t )$and$0$for$t$inthegivenfunctionyields＄19.36=-16(0{)}^2+b$, or ＄19.36 = b$.Substituting＄19.36$ for $b$ in function $h$ yields $h(t)=-16t^2+19.36$. When the ball reaches the floor, its height is ＄0$feetabovethefloor.Substituting＄0$ for $h(t)$ yields $0=-16t^2+19.36$. Adding ＄16 t^{2}$tobothsidesofthisequationyields＄16t^2=19.36$. Dividing both sides of this equation by ＄16$yields$t^{2} = 1.21$.Takingthepositivesquarerootofbothsidesofthisequationyields$t = 1.1$.Therefore,thefunctionestimatesthattheballwillreachthefloor＄1.1$ seconds after being released. Note that 1.1 and 11/10 are examples of ways to enter a correct answer.