Quadratics from Word Problems

The area of a playground is 336 yd2 . The width of the playground is 5 yd longer than its length. Find the length and width of the playground

•  length = 26 yd, width = 21 yd
• length = 21 yd, width = 26 yd 
• length = 21 yd, width = 16 yd 
• length = 16 yd, width = 21 yd

Suppose that the equation
V = 20.8x² – 458.3x + 3,500 represents the value of a car from 1964 to 2002. What year did the car have the least value? (x = 0 in 1964) 

• 1965
• 1970
• 1975
• 1980

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  (if air resistance is neglected). When will the object reach its maximum height?

• 4 ft
• 0 seconds
• 0 ft
• 4 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

Solve the word problem:  How high would you jump if the equation for jumping from a cliff is:    h(t) = -16t² + 8t + 24?

• 25
• 24
• 8
• 26

A diver is standing on a platform above the pool. He jumps form the platform with an initial upward velocity of 8 ft/s. Use the formula
h(t) = −16t² + 8t + 24, where h is his height above the water, t is the time, v is his starting upward velocity, and s is his starting height. How high is the platform?

• .25 ft
• 24 ft
• 25 ft
• 8 ft

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

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

One leg of a right triangle is seven more than the other leg. The hypotenuse is eight more than the shorter leg. Find the lengths of the longest side.

• 5 ft
• 3 ft
• 12 ft
• 13 ft

What is the smallest of 3 consecutive positive integers if the product of the smaller two integers is 5 less than 5 times the largest integer? 

• 10
• -5
• 5
• -10