Quadratic function word problems (ACT) practice

A football is kicked straight up from a stadium deck. Its height $d$, in feet, above the playing field $t$ seconds after the kick is modeled by $d(t) = -16t^2 + 64t + 48$. What is the height of the football, in feet, $3$ seconds after it is kicked?

A ball is thrown straight upward from a platform. Its height $h$, in feet, above the ground $t$ seconds after it is thrown is modeled by $h(t) = -16t^2 + 32t + 20$. According to the model, what is the initial height of the ball above the ground, in feet?

A warehouse tracks inventory with $I(t) = -2t^2 + 6t + 85$, where $I(t)$ is the number of units on hand $t$ weeks after a shipment arrives. According to the model, how many units were on hand when the shipment arrived?

A decorative fountain shoots water straight up. The water's height $f$, in feet, above the nozzle $t$ seconds after leaving the nozzle is modeled by $f(t) = -2t^2 + 12t + 20$. What is the height of the water, in feet, $3$ seconds after it leaves the nozzle?

A theater's daily ticket revenue $R$, in dollars, when each ticket costs $p$ dollars is modeled by $R(p) = -3p^2 + 90p$. According to the model, what is the daily revenue, in dollars, when each ticket costs $10$?

A town's population $P$, in thousands, $t$ years after a census is modeled by $P(t) = -t^2 + 14t + 120$. According to the model, what is the population, in thousands, $6$ years after the census?

A parabolic bridge arch has height $h$, in meters, at a horizontal distance $x$ meters from the left pillar modeled by $h(x) = -x^2 + 10x + 15$. According to the model, what is the height, in meters, of the arch $8$ meters from the left pillar?

A company's daily profit $P$, in dollars, when $n$ hundred items are sold is modeled by $P(n) = -n^2 + 18n + 36$. According to the model, what is the daily profit, in dollars, when $4$ hundred items are sold?