Rate of Change of Quadratic Functions

Calculate the average rate of change of the function f(x) = 2x^2 - 3x + 5 over the interval [1, 3].

• 5

• 3

• 10

• 7

Find the average rate of change of the function g(x) = -x^2 + 4x - 1 over the interval [2, 5].

• -3

• 2

• 5

• 10

Determine the average rate of change of the function h(x) = 3x^2 + 2x - 7 over the interval [-2, 2].

• -2

• 10

• -10

• 2

What is the average rate of change of the function k(x) = x^2 - 6x + 9 over the interval [3, 5]?

• 0

• 4

• 2

• 3

Two functions are shown below. Quadratic function, f(x), is represented in the graph below. Quadratic function, g(x), is represented in the table. Which function has a greater average rate of change over the interval -2 < x < 1?

• f(x)

• g(x)

Answer explanation

The graph shows a ball thrown into the air. What is the average speed of the ball going up (in feet per second)? (Hint: Calculate the Average Rate of Change between the y-intercept and the vertex (0

Mathematical Equivalence

OFF

The graph shows a ball thrown into the air. What is the average speed of the ball going up (in feet per second)?

(Hint: Calculate the Average Rate of Change between the y-intercept and the vertex (0<x<2). Enter a number between 0 and 100.)

Mathematical Equivalence

OFF

What is the average rate of change from x=0 to x=1

• -3

• 3

• 0

• 2

What is the rate of change from [-2,0]

• 2

• 4

• 0

• -2

What is the rate of change of f(x) over the interval [0, 2]?

• -2

• 2

• 3/2

• 2/3