Modeling With Quadratics

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

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

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

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

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

Determine which function the set of ordered pairs best represents.
{(-2, 2), (-4, 4), (2, 2), (4, 4)}

• linear

• exponential

• quadratic

Which function has the highest range with a domain of 3?

• f(x) = 2x - 4

• g(x) = 2(0.5)^x

• h(x) = 3x² + 4x + 9

How would you change the graph of f(x) = x² to produce the graph of g(x) = x² - 4?

• shifts the graph f(x) down 4 units

• shifts the graph f(x) up 4 units

• shifts the graph f(x) left 4 units

• reflects the graph of f(x)

What transformation changed the graph of f(x) = x² to the graph shown?

• horizontal translation

• vertical translation

• reflection

• vertical stretch

Graph: f(x) = -2x² + x + 1

• Graph A

• Graph B

• Neither