Quadratic Word Problems Worksheet with Answers

Name: KEY Date: 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 is the time in seconds and his the height in feet. a. How long did it take for Jason to reach his maximum height x = (- b)/(2a) = - 16/(2(k)) + (- k)/- 32 = 1/2 = 0.5 Co.5 seconds. b. What h(0.5) = - 16 * (0.5) ^ 2 + 16(0.5) + 480 = underline 484f+ 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? x = - 128/(2(- 16)) = - 128/- 32 = boxed 4seconds b. What h(4) = - 16 * (4) ^ 2 + 128(4) = boxed 256f+ 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(- 10)) = - 12/32 = 0.375 sec h(0.375) / - 16 * (0.375) ^ 2 + 12(0.375) =2.25 f+ No you will not be able to alpha*un * K' 4. Find a, b and e so that the parabola whose equation is y = a * x ^ 2 + bx + c has its vertex at (3,2) and passes through the point (-1,10) y = a * (x - 3) ^ 2 + 2 10 = a * (- 1 - 3) ^ 2 + 2 10 = a * (- 4) ^ 2 + 2 10-162 +2 8 = 16a a = 1/2 y = 1/2 * (x - 3) ^ 2 + 2 = 1/2 * (x ^ 2 - 6x + 9) + 2 = 1/2 * x ^ 2 - 3x + 9/2 + 2 y = 1/2 * x ^ 2 - 3x + 13/2 5. A small independent motion picture company determines the profit Pfor producing n 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. How many DVDs should the company produce to maximize the profit? x= -3,40 2(- 0.02) = - 3.4/- 0.04 / 85 85 thousand DVDs b. What will the maximize profit be? P(85)=-0.02(85)²+3.40(855)-16= 128.5 thousand 6. 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? left b. How long is the ball above 7 meters? to seconds x = - 8/(2(- 1)) = - 8/- 2 = 4 h(4) = - (4) ^ 2 + 8(4) h(4) = - 16 + 32 h(4) = 16 c. List all the transformation from the parent graph h(t) = x ^ 2 height (meters) Transformations Y = - (x - 4) ^ 2 + 16 -reflect across x-axis -horizontal chift right 4 units -vertical shift up 16 units 2345 478 lime (seconds) The following equation represents the path of a donut hole being thrown by Ms. Doll where x represents the time the donut is in the air and y represents the height 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. x = - 4/(2(- 1)) = - 4/- 2 = 2 y = - (2) ^ 2 + 4(2) - 2 =-4+8-2 4-2 2 V / (2, 2) Pts: (2,2) (1,1) (3,1) V b. At what time does the donut reach its maximum height? X= 2 seconds c. What is the maximum height of the donut? 2f + d. Rewrite the equation in vertex form, then list all the transformations of the graph from the parent function y^ ominus x ^ 2 Y = - (x - 2) ^ 2 + 2 Transformations: -reflect x-axis. horizontal shift right 2