Application of Quadratics

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?

• -1

• 5

• 11

• 25

• 50

April shoots an arrow upward at a speed of 80 ft/sec from a platform of 25 ft. high. The pathway of the arrow can be represented by the equation h = -16t² + 80t + 25, where h is the height and t is the time in seconds. What is the maximum height that the arrow reaches?

• 80 ft.

• 90 ft.

• 140 ft.

• 125 ft.

A toy rocket is launched and its height is modeled by the equation h = -16t² + 32t + 48. What is the initial heigh of the object?

• 48 ft.

• 16 ft.

• 32 ft.

• 2 ft.

An object in launched directly upward and the height of the object is represented by the equation s(t) = –16t² + 64t + 80. What is the initial velocity the object is launched at?

• 64 feet

• 80 feet

• 16 feet

• -16 feet

A lizard is jumping across the water in search of food. The equation h = -12t² + 6t models the lizard's height in feet above the water t seconds after he jumps. How long after jumping is he back on the water?

• 0.1 seconds

• 0.25 seconds

• 0.50 seconds

• 0.75 seconds

• 1 second

Fireworks are fired from the roof of a 100-foot building. The equation h = -16t² +84t + 100 models the height, h, of the fireworks at any given time, t. How high do the fireworks get?

• 2.625

• 6.25

• 100

• 200

• 210.25

If the graph shows price vs profit, what is the maximum profit? 

• 35

• 12,000

• 12,500

• 60

A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h=-16t² + 90t gives the height h of the ball after t seconds.
What is the maximum height of the ball?

• 126.56 ft

• 5.625 sec

• 2.81 sec

• 90 ft

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?

• 4 ft

• 0 seconds

• 0 ft

• 4 seconds

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?

• only at t = 0 seconds 

• only at t = 3 seconds

• only at t = 9 seconds

• at both t = 0 seconds and t = 3 seconds