Quadratic Modeling Worksheets Grade 10

1. A company's profit from selling x units of a product is modeled by the quadratic function P(x) = -2x² + 120x - 1000. How many units must the company sell to maximize its profit, and what is the maximum profit?
2. A company's profit P(x) = -2x² + 40x - 128, where x is units sold (in hundreds). Find the number of units that maximizes profit.
3. Hana launches a model rocket from the ground. The height h(t) in meters after t seconds is modeled by a quadratic function. The rocket reaches a maximum height of 144 meters at 6 seconds. Find the height of the rocket after 4 seconds.

…and 5 more problems

1. Liam is designing a rectangular garden next to a straight stone wall. He has 120 meters of fencing to enclose the other three sides of the garden (the side along the wall does not need fencing). Liam wants to maximize the area of the garden. What dimensions (length parallel to the wall and width perpendicular to the wall) will give the maximum area, and what is that maximum area?
2. Matiu is designing a water fountain for a public park. The water stream from the fountain follows a parabolic path. The height of the water (in meters) above the nozzle is modeled by the quadratic function h(x) = -0.02x² + 0.8x + 1.2, where x is the horizontal distance from the nozzle in meters. Matiu wants to know the maximum height the water reaches and the horizontal distance at which this maximum height occurs. What is the maximum height of the water stream?
3. A parabolic arch bridge spans a river with its vertex at the highest point of the arch. The arch is modeled by the quadratic function h(x) = -0.02x² + 24, where h(x) represents the height in meters above the water level and x represents the horizontal distance in meters from the center of the arch. The bridge's supports are located where the arch meets the water (h(x) = 0). What is the total span of the bridge between these two support points?

…and 4 more problems

1. A company's profit P(x) = -2x² + 80x - 600, where x is the number of units sold. Find the number of units that maximizes profit.
2. A rectangular garden has a perimeter of 60 meters. If the area is modeled by A(x) = x(30 - x), find the maximum possible area of the garden.
3. Ava is designing a parabolic arch for a new garden entrance. The arch will be made of steel and its height (in meters) above the ground at a horizontal distance x (in meters) from the left base is modeled by the quadratic function h(x) = -0.25x² + 3x + 1.5. The arch is supported by two vertical pillars at the left and right bases where the arch meets the ground. Determine the maximum height of the arch and the horizontal distance from the left base where this maximum height occurs.

…and 4 more problems