ALG Quadratic Applications

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation 
s(t) = –16t² + 64t + 80.
What will be the object's maximum height? 

• 2 ft

• 80 ft

• 144 ft

• 64 ft

When I want to find the maximum or minimum height of an object, I should_____

• Set the equation = 0 and solve.

• Use x = (-b/2a) as my answer.

• Substitute x = 0 into the equation.

• Find the y-coordinate for the vertex.

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

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

• 9 seconds

240 ft

256 ft

265 ft

230 ft

• 240 ft

• 256 ft

• 265 ft

• 230 ft

• A
• B
• C
• D

• The speed of the rocket was greatest at about 6 seconds after it was fired.

• The rocket traveled 180 meters.

• The rocket reached its maximum height in about 6 seconds.

• The rocket returned to the ground in about 6 seconds.

A mathematician used data of the average gas mileage in new vehicles in Rome for the years 2012 to 2022 to create a quadratic function that models the data, where x is the number of years since 2012 and y is average gas mileage in miles per gallon. Some of the values are shown in the table. During what years was the average gas mileage decreasing?​ ​ (a)   <x<​ (b)  

• 2016

• 2022

• 2026

• 0

• 16

• 2021

• 9

• 10

Which answer choice describes  y = -3x² +7x - 2 accurately?

• opens up with a maximum

• opens up with a minimum

• opens down with a maximum

• opens down with a minimum 

For which interval is the height of the ball always decreasing? 

• 0≦x≦2.5

• 0<x<5.5

• 2.5<x<5.5

• x≧2