Quadratic Inequalities Answers

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

Carmen is using the quadratic equation (x + 15)(x) = 100 where x represents the width of a picture frame. Which statement about the solutions x = 5 and x = –20 is true?

A soccer ball is kicked into the air from the ground. If the ball reaches a maximum height of 25 ft and spends a total of 2.5 s in the air, which equation models the height of the ball correctly? Assume that acceleration due to gravity is –16 ft/s2.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 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?

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 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 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?