Modeling with Quadratic Equations Answers

A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t2 + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s. Which solution can be eliminated and why?

A softball pitcher tosses a ball straight upward from a height of 3 feet above the ground with an initial velocity of 50 feet per second. The acceleration due to gravity is –16 ft/s².Which quadratic equation represents the height of the ball above the ground after t seconds?h(t) = at2 + vt + h0

A rectangular pan has a length that is the width. The total area of the pan is 432 in.2. What is the width of the cake pan?A = lw

A car’s stopping distance in feet is modeled by the equation where v is the initial velocity of the car in miles per hour and f is a constant related to friction. If the initial velocity of the car is 47 mph and f = 0.34, what is the approximate stopping distance of the car?

A baseball is thrown into the air from a height of 5 feet. The ball reaches a maximum height of 43.5 feet and spends a total of 3.2 seconds in the air. Which equation models the height of the baseball? Assume that acceleration due to gravity is –16 ft/s2.

A firework is launched into the air from ground level with an initial velocity of 128 ft/s. If acceleration due to gravity is –16 ft/s2, what is the maximum height reached by the firework?h(t) = at2 + vt + h0

A box is to be constructed with a rectangular base and a height of h cm. The length, l, of the box is 10 cm, and the width, w, is twice the height. Which quadratic equation best models the volume of the box? V = lwh

The owner of an office building is expanding the length and width of a parking lot by the same amount. The lot currently measures 120 ft by 80 ft, and the expansion will increase its area by 4,400 ft2. By how many feet should the length of the parking lot be increased?A = lw

A projectile is launched straight up from the ground with an initial velocity of 120 ft/s. If acceleration due to gravity is –16 ft/s2, after about how many seconds will the object reach a height of 200 ft?h(t) = at2 + vt + h0

The Davidson family wants to expand its rectangular patio, which currently measures 15 ft by 12 ft. They want to extend the length and width the same amount to increase the total area of the patio by 160 ft2. Which quadratic equation best models the situation?A = lw