ACT Functions Practice Questions

A film's profit (in millions of dollars) can be modeled by the quadratic function $P(x) = -x^2 + 5x - 4$, where $x$ is the number of weeks since release. After how many weeks does the film first break even (i.e., when does profit first reach zero)?

A film's profit (in millions of dollars) can be modeled by the quadratic function $P(x) = -x^2 + 5x - 4$, where $x$ is the number of weeks since release. After how many weeks does the film first break even (i.e., when does profit first reach zero)?

A delivery truck's route time can be modeled by the function $T(d) = 0.5d + 1$, where $T$ is the total time in hours and $d$ is the distance traveled in miles. If the truck needs to complete a delivery in exactly 3 hours, what is the maximum distance it can travel?

A delivery truck's route time can be modeled by the function $T(d) = 0.5d + 1$, where $T$ is the total time in hours and $d$ is the distance traveled in miles. If the truck needs to complete a delivery in exactly 3 hours, what is the maximum distance it can travel?

A delivery truck's route time can be modeled by the function $T(d) = 0.5d + 1$, where $T$ is the total time in hours and $d$ is the distance traveled in miles. If the truck needs to complete a delivery in exactly 3 hours, what is the maximum distance it can travel?

A delivery truck's route time can be modeled by the function $T(d) = 0.5d + 1$, where $T$ is the total time in hours and $d$ is the distance traveled in miles. If the truck needs to complete a delivery in exactly 3 hours, what is the maximum distance it can travel?

A clothing store sells shirts where the profit per shirt is modeled by the quadratic function $P(x) = -2x^2 + 32x - 96$, and the cost per shirt is modeled by the linear function $C(x) = 4x + k$. For what value of $k$ do the profit and cost functions intersect at exactly one point?

A town's budget allocates funds for parks based on the function $f(x) = -x^2 + 8x - 12$, where $x$ represents the percentage of budget allocated (0 ≤ x ≤ 10) and $f(x)$ is the resulting quality score. What is the maximum quality score achievable within the allowed allocation range?

A restaurant's daily profit (in dollars) from selling lunch specials is modeled by the quadratic function $P(n) = -2n^2 + 60n - 250$, where $n$ is the number of specials sold each day. To find the maximum daily profit, first determine the vertex of the parabola. What is the y-coordinate of the vertex?

A restaurant's daily revenue $R(p)$, in dollars, from selling a dish at price $p$ dollars is given by $R(p) = -2p^2 + 40p - 120$. What price should the restaurant charge to maximize its daily revenue from this dish?