Modeling with Quadratic Equations Answers

Both Rachel and Dominique throw tennis balls into the air. At any time, t, the height, h, of Rachel’s ball is modeled by the equation h = –16t2 + 30t + 5. Dominique throws his tennis ball with the same acceleration, a, from the same initial height, , but with an initial velocity, v, double that of Rachel’s. Which equation best models the height of Dominique’s tennis ball?h(t) = at2 + vt + h0

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?

Two children are throwing a baseball back and forth. The ball is 4 ft above the ground when it leaves one child’s hand with an upward velocity of 36 ft/s. If acceleration due to gravity is –16 ft/s2, how high above the ground is the ball 2 s after it is thrown?h(t) = at2 + vt + h0

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

The main cable of a suspension bridge forms a parabola modeled by the equation y = a(x – h)2 + k where y is the height in feet of the cable above the road, x is the horizontal distance in feet from the right bridge support, a is a constant, and (h, k) is the parabola’s vertex. What is the maximum and minimum height of the bridge modeled by the equation y = 0.005(x – 60)2 + 8?

Justin and Elena each launched a toy rocket into the air. The height of Justin’s rocket is modeled by the equation h = –16t2 + 60t + 2. Elena launched his rocket from the same position, but with an initial velocity double that of Justin’s. Which equation best models the height of Elena’s rocket?h(t) = at2 + vt + h0

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 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

When using a quadratic equation in the form y = ax2 + bx + c to model the height of a projectile (y) over time (x), which of the following is always represented by the constant term?

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