Discriminant Analysis Worksheets Grade 9

1. A company's revenue from selling x units of a new gadget is modeled by the quadratic function R(x) = -3x² + 150x + 2000. The marketing team wants to know if they can achieve a revenue of exactly $5000. Using the discriminant of the quadratic formula, determine whether this revenue level is possible.
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 if they can achieve a profit of exactly $500. Using the discriminant of the quadratic formula, determine whether this profit level is possible and explain what this means about the number of units they would need to sell.
3. A company's revenue from selling x units of a product is modeled by the quadratic function R(x) = -3x² + 150x - 1800. The company wants to determine if they can achieve a revenue of exactly $1000. Using the discriminant of the quadratic formula, determine whether this revenue level is possible.

…and 4 more problems

1. Aroha is a park ranger monitoring the flight of a hawk. The hawk's height above the ground, in meters, t seconds after it begins its dive is modeled by the quadratic function h(t) = -5t² + 36t + 12. Aroha needs to determine if the hawk will ever reach a height of exactly 80 meters during its dive. Using the discriminant of the quadratic formula, determine whether this height is achievable.
2. A drone is launched from a platform 20 meters high with an initial upward velocity of 15 m/s. The drone's height above ground is modeled by the equation h(t) = -5t² + 15t + 20, where t is time in seconds. Determine how many seconds it will take for the drone to reach the ground.
3. A drone is launched from a platform 12 meters high. Its height above ground is modeled by the function h(t) = -2t² + 8t + 12, where t is time in seconds. The drone operator needs to know if the drone will clear a tree that is 20 meters tall. Using the discriminant, determine whether the drone reaches a height of at least 20 meters at any point during its flight.

…and 4 more problems

1. Mason launches a model rocket from the ground with an initial upward velocity of 30 m/s. The height of the rocket above the ground, in meters, is modeled by the quadratic function h(t) = -5t² + 30t, where t is the time in seconds after launch. Isabella, his classmate, claims the rocket will reach a height of exactly 50 meters during its flight. Using the discriminant of the quadratic equation, determine whether Isabella is correct.
2. x² + 6x + 1 = 0
3. Emma sketches the graph of the quadratic function f(x) = 5x² - 20x + 15. The parabola opens upward. Calculate the discriminant of this quadratic equation and determine how many real x-intercepts the graph has.

…and 4 more problems