Quadratic Profit Gravity

The function f(t) = -5t²+20t + 60 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

• 4 seconds

• -2 seconds

• -6 seconds

• 6 seconds

The profit from selling local ballet tickets depends on the ticket price.  Using past receipts, we find that the profit can be modeled by the function p= -15x² +600x +60 , where x is the price of each ticket.  What is the maximum profit you can make from selling tickets?

• $6060
• $20
• $600
• $10,250

A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by the equation h = -6t² + 6t where h is the frog's height at any given time, t . How many seconds until the frog is back on the ground?

• 0.5 seconds

• 1 second

• 1.5 seconds

• 2 seconds

• 3 seconds

The quadratic equation 0 = -16t² + 80t gives the time t in seconds when a golf ball is at a height of 0 feet. How do you find how long the golf ball is in the air?

• find the y -coordinate of the maximum

• find the x-coordinate of the maximum

• find the solution

• find the zero

• Use the table to find the y-intercept

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? (choose carefully!)

• 10 seconds

• 64 seconds

• 960 seconds

• 2 seconds

The profit from selling local ballet tickets depends on the ticket price.  Using past receipts, we find that the profit can be modeled by the function p= -15x² +600x +60 , where x is the price of each ticket.  What is the maximum profit you can make from selling tickets?

• $6060
• $20
• $600
• $10,250

What is the domain of the parabola created by the ball?

• Domain : 0 ≤ d ≤ 280
• Domain : 0 ≤ h ≤ 150
• Domain : 0 ≤ d ≤ 570
• Domain : 0 ≤ h ≤ 280

John hits a fly ball into the air. The ball reaches a maximum height of 200 ft after 4 seconds. What is a reasonable domain of the fly ball?

• All real numbers between 0 feet and 200 feet
• All real numbers between 0 feet and 400 feet
• All real numbers between 0 seconds and 4 seconds
• All real numbers between 0 seconds and 8 seconds

Find the range of the function

f(x) = x² + 12. (Hint: think maximum or minimum)

• y ≤ 12

• y ≥ 12

• x ≥ 0

• y > 0

Alain throws a stone off a bridge into a river below. The stone's height (in meters above the water), x seconds after Alain threw it, is modeled by:

h(x)= -5x² + 10x + 15

How many seconds after being thrown will the stone hit the water?

• -1 seconds
• 1 second
• 2 seconds
• 3 seconds