Quadratic Applications Worksheets Grade 9

1. A parabolic arch bridge spans a river with its vertex at the water's surface. The arch is modeled by the quadratic function f(x) = -0.02x² + 12, where x represents the horizontal distance from the center of the arch in meters, and f(x) represents the height above the water in meters. A boat needs to pass under the bridge with a clearance of at least 2 meters. What is the maximum width of the boat that can pass through the center of the arch while maintaining this clearance?
2. Nova throws a ball straight upward from a platform 6 meters above the ground. The height of the ball above the ground, h(t) in meters, after t seconds is given by the quadratic function h(t) = -5t² + 16t + 6. The graph of this function is a parabola opening downward, with the vertex representing the maximum height of the ball. After how many seconds does the ball reach its maximum height, and what is that maximum height?
3. Emma throws a ball straight upward from a height of 1 meter above the ground with an initial velocity of 15 m/s. The height of the ball above the ground after t seconds is modeled by the quadratic function h(t) = -5t² + 15t + 1, where h(t) is in meters. How many seconds after the throw does the ball hit the ground? Round your answer to the nearest tenth of a second.

…and 2 more problems

1. Mason is designing a water fountain that shoots a stream of water into the air. The height of the water stream above the fountain's nozzle, in meters, is given by the quadratic function h(t) = -5t² + 18t + 2, where t is the time in seconds after the water leaves the nozzle. On a coordinate grid, the path of the water forms a parabola. What is the maximum height, in meters, that the water stream reaches above the nozzle?
2. A parabolic arch bridge has its vertex at (0, 20) and spans a horizontal distance of 40 meters, with the endpoints at (-20, 0) and (20, 0). The arch follows a quadratic function in the form y = ax² + bx + c. What is the height of the arch 10 meters from the center?
3. Emma kicks a soccer ball whose height is given by h(t) = -5t² + 15t + 10. What is the maximum height of the ball?

…and 4 more problems

1. A water fountain at a park shoots water into the air from a nozzle at ground level. The height of a water droplet, in meters, is given by the function h(d) = -0.05d² + 0.9d, where d is the horizontal distance from the nozzle in meters. Aroha notices that the stream of water forms a perfect parabolic arc. She wants to place a small cup at the highest point of the arc to catch a falling leaf. What is the maximum height of the water stream, and at what horizontal distance from the nozzle does this occur?
2. Mere kicks a soccer ball whose height is given by h(t) = -16t² + 48t + 4. Find the maximum height the ball reaches.
3. Aroha kicks a soccer ball whose height is given by h(t) = -5t² + 15t + 2. Find the maximum height of the ball.

…and 5 more problems