Quadratic Application Word Problems

Name: Key Date: 4.5 Quadratic Application Word Problems 1. Jason jumped off of a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h(t) = - 16t ^ 2 + 16t + 480 where t is the time in seconds and his the height in feet. t =sec(x-velxe) a. How long did it take for Jason fad t zeta = - 16/(2(- 16)) > - 16/(- 3z) =- 1 2 Rightarrow x= 1 2 sec b. What was the highest point that Jason reached? h(1/4) = - 16 * (- 4) ^ 2 + 16(1/2) + 460 h(t)=4 int - 4ft c. What was Jason's h(0) = - 16 * (0) ^ 2 + 16(0) + 650 h(u) = 4 * 50ft 2. If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h, after t seconds is given by the equation h(t) = - 16t ^ 2 + 128t (air resistance is neglected) a. How long will it take the rocket to hit its maximum height? -128 X=2(14) -125 -12 →x=4sec b. What is the maximum height h(4) = - l * 6 * (4) ^ 2 + 12r(4) 6(x) = 256f c. How long did take for the rocket to reach the ground? 0 = - 16t ^ 2 + 127t 0 = - 16t(t - 8) f - y = 0 [f^ prime Phi re.c ] 3. You are trying to dunk a basketball. You need to jump 2.5 ft in the air to dunk the ball. The height that your feet are above the ground is given by the function h(t) = - 16t ^ 2 + 12t What is the maximum height your feet will be above the ground? Will you be able to dunk the basketball? X = - 12/(2(- 16)) = - 12/- 32 = boxed 3 gamma 524 n( 3 8 )= underline - 16 * (3/7) ^ 2 + 12(7/7) h( 1 r )= boxed 2 1/4 * ft اگر max height Imed to be 2.5 ft in the ait I'm only reading a height of 2.25 ft. I will not be able to dunk. 4. A ball is thrown in the air. The path of the ball is represented by the equation h(t) = - t ^ 2 + 8t Graph the equation over the interval 0 < t < 8 on the following graph. a. What is the maximum height of the ball? h. How long is the ball above 7 meters? Rewrite the equation in vertex form. height (meters) 20 15 10 5 time (seconds) -४ a.) x 21 4sec ln(4) = - 4 ^ 2 + 5(4) h(4)=16f1h 6 *) r^ 7 = - t ^ 2 + 8t log^ k + 0 = - t ^ 2 * r*gamma*t - 7 0 = t ^ 2 - rt + 1 0 = (t - 7)(t - 1) 0=t-7 0 = t - 1 t=7sect-Isec these are the times when the ball will be 7m in the air. Therefore the ball will be above 7m for sec. c) h(t) = - t ^ T + gamma*E h(t) = - (t ^ 2 - t + 16) + 16 h(t) = - (t - 4) ^ 2 + 16 7. The following equation represents the path being thrown by Mr. London where x represents the time (in seconds) the donut is in the air and y represents the height (in feet) of the donut. y = - x ^ 2 + 4x - 2 a. Graph the equation to show the path of the donut hole, show at least three points. 10 X = - 4/(2(- 1)) = 2 y = - (2) ^ 2 + 4(2) - 2 y = - 4 + gamma - 2 y = 2 vertex @ (2,2) b. At what time does the donut reach its maximum height? y = - x ^ 2 + 4x - 2 x = - 4/(2(- 1)) = boxed 25ec c. What is the maximum height of the donut? y = - (z) ^ 2 + 4(z) - 2 y = 2ft d. Rewrite the equation in vertex form. y = - x ^ 2 + 4x - 2 y = - (x ^ 2 - 4x + 4) - 2 + 4 y = - (x - 2) ^ 2 + 2 5. A small independent motion picture company determines the profit Pfor producing a DVD copies of a recent release is P = - 0.02n ^ 2 + 3.4n - 16 Pis the profit in thousands of dollars and nis in thousands of units. K_{1}*y -> (n, r) How many DVDs should the company produce to maximize the profit? find n. vertex n= - 3.4/(2(- 0.02)) * -3.40 -..44 n = 85bv * b ^ 1 * s b. What will the maximize profit be? vertex P = - 0.02 * (75) ^ 2 + 3.4(77) - 16 p =\$ 2 5.50