Quadratic Modeling

An experiment examined the relationship between the number of miles a car traveled, y, per gallon of gasoline and the speed of the car, x, in miles per hour. The table displays the data collected.

A quadratic function can be used to model the data in the table. Which value best estimates the miles per gallon when the speed is 65 miles per hour?

• 27.9

• 31.0

• 40.2

• 24.9

Which function best models the data?

• A

• B

• C

• D

Q32

• y = 0.001x² - 0.426x + 35.672

• y = -0.60x² + 348.1x - 334.2

• y = 0.001x² + 35.672

• y = -0.60x² - 334.2

• A

• B

• C

• D

TEK A.8 (B)

• d(x) = 0.05x² + 0.74x

• d(x) = 0.05x² + 0.74x + 9.17

• d(x) = 0.26x² – 3.11x

• d(x) = 0.26x² – 3.11x + 1

The data can be modeled by the quadratic function

y = ​ (a)  

• A

• B

• C

• D

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