Quadratic Equations in Context

An golf ball in launched directly upward at 64 feet per second (ft/s) from a platform at Top Golf. Its height is represented by the equation

s(t) = –16t² + 64t + 80

What will be the golf ball's maximum height in feet? Enter a number only.

An golf ball in launched directly upward at 64 feet per second (ft/s) from a platform at Top Golf. Its height is represented by the equation

s(t) = –16t² + 64t + 80

What is the height of the platform at top golf?

• 16 feet

• 64 feet

• 80 feet

• 144 feet

An golf ball in launched directly upward at 64 feet per second (ft/s) from a platform at Top Golf that is 80 feet high. Its height is represented by the equation

s(t) = –16t² + 64t + 80

How long did it take for the golf ball to reach it's maximum height?

• 1 second

• 2 seconds

• 3 seconds

• 4 seconds

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?

• 0.42 seconds, 0.21609 meters
• 0.42 seconds, 0.21 meters
• 0.21 seconds, 0.42 meters
• 0.21 seconds, -2.058 meters

A fish jumping out of the water can be modeled by the function h(t) = -16t² + 43t - 6 where h(t) represents the height of the fish after t seconds. An eagle nearby spots the fish and dives to catch it; its flight path is modeled by the function h(t) = 27 - 13t. After how many seconds does the eagle catch the fish and at what height above the water?

• 0.75 seconds & 17.25 feet above the water

• 1.34 seconds & 22.89 feet above the water

• 2.75 seconds & 8.75 feet above the water

• The eagle doesn't catch the fish.

​ (a)   ​ (b)   ​ (c)   ​ (d)   ​ (e)  

• x-intercept/roots at (-3,0) and (1,0)

• vertex of (-1,4)

• y-intercept at (0,3)

• maximum at y = 4

• axis of symmetry at x = -1

• minimum at y = 4

• y-intercept at (0, -3)

• axis of symmetry at x = 4

• roots at (3,0)

• vertex at (4,-1)

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 

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

Analyze the given graph and the determine the correct function.​ (a)   ​ (b)  

• x(x-2)

• x+(x-2)

• (x+4)(x+5)

• (x-0)