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 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 skydiver jumps from an airplane at an altitude of 2,500 ft. He falls under the force of gravity until he opens his parachute at an altitude of 1,000 ft. Using the initial velocity of zero, approximately how long does the jumper fall before he opens his chute?For this quadratic model we will let the y-axis be the axis of symmetry.h(t) = -16t2 + vt + h0

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

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

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

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

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 total area of two square windows is 1,025 in.2. Each side of the larger window is 5 in. longer than the sides of the smaller window. How long are the sides of the smaller window?A = s2

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?