Quadratic Function Word Problems

A company's revenue R from selling x items can be modeled by the equation R = -2x² + 120x - 100. How many items must they sell to maximize their revenue?

• 15 items

• 30 items

• 60 items

• 120 items

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.

h = -5t² + 45

When is the ball at ground level?

If you square 5 more than a positive number, the result is 88 more than 12 times the number. Find the numbers.

• -9 and 7

• 9 and -7

• 15 and -5

Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air. The equation h = -2t² + 7t + 4 models the toy's height, h, from the ground at t seconds after he threw it. How high is the toy after 1 second?

The height, y, of a ball tossed into the air can be represented by the equation

y = −x² + 10x + 3, where x is the elapsed time. What is the equation of the axis of symmetry of this parabola?

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation h(t) = -16t² +128t When will the object reach its maximum height?

A ball is thrown into the air with an upward velocity of 100 ft/s. Its height, h, after t seconds is given by the function

h = -16t² + 64t + 960.

How many seconds did it take for the ball to reach its maximum height?

Amelia runs a catering business. Based on her records, her profit is shown by P = 2x² - 44x -150, where x is the number of meals she caters and P is her profit. When P is negative, Amelia loses money. What is the least number of meals Amelia needs to cater in order to begin making profit?

A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. What is the maximum height the rock reaches ?

• 1.094 ft

• 174.141 ft

• 155 ft

• 4.393 ft

• None of the above

A kid launches a rock off of a cliff. The height of the rock after t seconds can be modeled by the graph shown. When does the rock hit the ground?

• 1.094 seconds

• 174.141 seconds

• 155 seconds

• 4.393 seconds

• None of the above