Quadratic Formula Worksheets Grade 9

1. Solve: 5x² - 14x + 8 = 0 using quadratic formula
2. A company's profit from selling x units of a product is modeled by the quadratic function P(x) = -2x² + 120x - 1000. The company wants to determine the number of units they need to sell to break even (make zero profit). How many units must they sell to break even?
3. Ava is analyzing the trajectory of a water fountain in a park. The height of a water droplet (in meters) above the fountain's nozzle is modeled by the equation h(t) = -7t² + 91t + 42, where t is the time in seconds after the droplet leaves the nozzle. How many seconds after leaving the nozzle does the water droplet hit the ground? Round your answer to two decimal places.

…and 5 more problems

1. Emma is designing a skateboard ramp that forms a parabolic path. The ramp's height above ground follows the equation h(t) = -2t² + 12t, where h is the height in feet and t is the time in seconds after launch. At what time does the skateboard reach its maximum height?
2. Emma is analyzing the flight path of a toy rocket launched from a platform. The rocket's height above the ground, in meters, is given by the quadratic equation h(t) = -5t² + 35t + 40, where t is the time in seconds after launch. How many seconds after launch does the rocket hit the ground?
3. Solve: 7x² + 12x - 2 = 0 using quadratic formula

…and 6 more problems

1. Sophia is designing a parabolic fountain for a park. The height of the water (in meters) above the fountain's nozzle is modeled by the equation h(t) = -4t² + 16t + 6, where t is the time in seconds after the water is ejected. At what time does the water hit the ground (height = 0)? Round your answer to one decimal place.
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. 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 are the dimensions of the garden?

…and 6 more problems