Quadratic Formula Worksheets Grade 9

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 break even (make zero profit)?
2. Aroha is designing a parabolic water fountain for a public park. The height of a water jet (in meters) above the fountain basin is modeled by the function h(x) = -0.2x² + 4x + 1.6, where x is the horizontal distance (in meters) from the nozzle. At what horizontal distance from the nozzle does the water jet hit the basin (where height is zero)?
3. Kaia is designing a parabolic water arc for a sculpture in a park. On a coordinate grid, the arc of the water is modeled by a quadratic function with its vertex at (0, 18). The water stream hits the ground at points (−9, 0) and (9, 0). Write the quadratic equation in standard form that models the arc, then use the quadratic formula to find the x-coordinates where the height of the arc is 10 units above the ground.

…and 4 more problems

1. A rectangular garden has a length that is 5 meters more than its width. If the area of the garden is 84 square meters, what is the width of the garden in meters? Use the quadratic formula to solve.
2. A company's profit P (in thousands of dollars) from selling x units of a product is modeled by the quadratic equation P = -2x² + 120x - 1000. How many units must the company sell to break even (make zero profit)?
3. Mason is constructing a parabolic water fountain for a school project. The height of the water stream, in meters, is given by the equation h(d) = -3d² + 12d + 7, where d is the horizontal distance from the nozzle in meters. At what horizontal distance(s) from the nozzle will the water stream be exactly 7 meters high?

…and 4 more problems

1. Solve: 9x² - 13x - 7 = 0 using quadratic formula
2. Solve: 7x² + 12x - 2 = 0 using quadratic formula
3. Solve: 5x² - 13x + 6 = 0 using quadratic formula

…and 6 more problems