Analyzing Zeros and Function Behavior

The video tutorial explains how to sketch the graph of the function f(x) = x^3 + 2x^2 - 8x. It covers determining the end behavior, finding zeros, analyzing behavior near each zero, and identifying points between zeros. The tutorial concludes with graphing the function using the calculated points.

What is the function we are graphing in this tutorial?

• f(x) = x^3 + 2x - 8

• f(x) = x^3 + 2x^2 - 8x

• f(x) = x^2 + 2x - 8

• f(x) = x^3 - 2x^2 + 8x

What is the end behavior of the function f(x) = x^3 + 2x^2 - 8x?

• The graph behaves like x^2

• The graph behaves like x^3

• The graph behaves like x^4

• The graph behaves like x

How do we find the zeros of the function f(x) = x^3 + 2x^2 - 8x?

• By graphing the function

• By using the quadratic formula

• By factoring and setting each factor to zero

• By solving x^2 + 2x - 8 = 0

What are the zeros of the function f(x) = x^3 + 2x^2 - 8x?

• 0, 2, -4

• 0, -4, 2

• 0, 4, -2

• 0, -2, 4

What is the behavior of the function near the zero at x = 0?

• The function is linear

• The function is quadratic

• The function is cubic

• The function is constant

What is the behavior of the function near the zero at x = -4?

• The function is quadratic

• The function is linear

• The function is constant

• The function is cubic

What is the behavior of the function near the zero at x = 2?

• The function is constant

• The function is cubic

• The function is quadratic

• The function is linear

What point is found between the zeros at x = 0 and x = -4?

• (-3, -15)

• (3, -15)

• (3, 15)

• (-3, 15)

What point is found between the zeros at x = -4 and x = 2?

• (1, 5)

• (-1, 5)

• (1, -5)

• (-1, -5)

What is the overall shape of the graph of f(x) = x^3 + 2x^2 - 8x?

• The graph is a parabola

• The graph is a straight line

• The graph is a circle

• The graph is a cubic curve