Creating Quadratic Mathematical Models

If you square 5 more than a positive number, the result is 88 more than 12 times the number.  Find the numbers.

• -9, 7
• √75
• 9, -7
• 15, -5

The product of two consecutive negative even integers is 24.  Find the integers.

• 6, 8
• 6, 4
• -6, -8
• -6, -4

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

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

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

A diver is standing on a platform above the pool. He jumps form the platform with an initi8al upward velocity of 8 ft/s. Use the formula h t = −16 t² + 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

A rectangle has an area of 24 square units. The width is 5 units less than the length. What is the length, in units, of the rectangle? 

• 6
• 8
• 3
• 19

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

• 25
• 24
• 8
• 26

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