Quadratics Modeling

Which function is quadratic?

• f(x)

• h(x)

• g(x)

A system that contains one linear function and one quadratic function can have 0, 1, or 2 solutions.

• True

• False

• Cannot be determined

• Nobody cares

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

Using the table to the left, write a curve of best fit using quadratic regression from your calculator.

Calculate the quadratic regression function for this table of values to the nearest tenth.

• f(x) =
   2x² - 9x + 10

• f(x)=
   3x² + 9x - 10

• f(x) =
   3.1x² - 9.2x - 10.3

• f(x) =
  2.1x² - 8.6x + 10.1

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

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?

• $20

• $6060

• $7,120

• $9,250

• $10,050

A dolphin jumps from the water at at initial velocity of 16 feet per second. The equation h = -8t² + 16t models the dolphin's height at any given time, t. What is the maximum height the dolphin jumps?

• 1 foot

• 5 feet

• 7 feet

• 8 feet

• 12 feet

Your friend passes you the ball during a soccer game. The height off the ground is modeled by the equation

h = -4t² + 12t. How high did the soccer ball get?

• 1.5

• 3

• 5

• 9

• 15

Determine the curve of best fit using quadratic regression on your calculator.

• y = -2.7x + 7.4

• y = 0.95x² - 2.08x - 0.75

• y = -.05x - 3.26

• y = 0.95x² + 2.08x + 0.75