Domain and Range Worksheets Grade 9

1. A drone delivery service uses a quadratic function to model the height of its drones during delivery flights. The height h(t) in meters above ground level is given by h(t) = -2t² + 16t + 20, where t is time in seconds after takeoff. What is the maximum height the drone reaches during its flight?
2. Sophia is analyzing the path of a drone delivering a package. The drone's height above the ground (in meters) is modeled by the quadratic function h(t) = -3t² + 18t + 9, where t is the time in seconds after launch. The drone can only release its package when it is at least 24 meters high to ensure a safe drop. The graph of this function is a parabola opening downward. Determine the time interval (in seconds) during which the drone is at or above the required height of 24 meters. Then, from the graph of the function, state the domain and range of h(t) for the entire flight from launch until it returns to the ground (height = 0).
3. Emma is designing a custom skateboard ramp for a local park. The ramp's cross-section follows a parabolic path modeled by the function h(x) = -0.5x² + 3x + 1, where h represents the height in feet above ground level and x represents the horizontal distance in feet from the ramp's starting point. The city requires that the ramp must be at least 4 feet high to accommodate advanced tricks. Over what interval of horizontal distance (in feet) will the ramp meet this height requirement?

…and 4 more problems

1. Isabella is analyzing the flight of a toy rocket launched from a platform. The rocket's height above the ground, in meters, is modeled by the function h(t) = -2t² + 12t + 7, where t represents time in seconds after launch. The rocket's camera can only take clear pictures when the rocket is at least 15 meters high. Sketch a graph of the function, then determine the time interval (in seconds) during which the rocket's camera can take clear pictures.
2. A quadratic function is graphed on a coordinate plane with its vertex at (2, -3) and passing through the point (4, 1). The parabola opens upward. What is the equation of this quadratic function in vertex form?
3. Emma is designing a rectangular garden with a fixed perimeter of 60 meters. She wants to model the area of the garden as a function of its width. If the width is represented by x meters, what is the maximum possible area the garden can have?

…and 4 more problems

1. Mason is analyzing the path of a water fountain's spray. The height of the water above the nozzle (in feet) is modeled by the quadratic function h(x) = -0.2x² + 2x + 2, where x is the horizontal distance (in feet) from the nozzle. The water hits a decorative wall that is 8 feet away from the nozzle. What are the domain and range of the function for this real-world scenario, considering only the water's path until it hits the wall?
2. The graph of f(x) = -3x² + 18x - 15 is a parabola opening downward with vertex at (3, 12) and x-intercepts at (1, 0) and (5, 0). What is the domain and range of this function?
3. f(x) = 2x² - 4x + 1, find f(3) = ?

…and 4 more problems