Question

Consider function f.

f(x)= x^3 + 2x^2 - 5x - 6

Select the locations of the zeros of function f on the coordinate plane. Then select the end behavior of its graph.

Answer 1

As x approaches negative infinity, f(x) approaches negative infinity

Step-by-step explanation: Plato

Answer 2

• x = 2, x = -1, x = -3

• As x approaches negative infinity, f(x) approaches negative infinity

Explanation:

Given function

• f(x)= x^3 + 2x^2 - 5x - 6

Finding zero's

• x^3 + 2x^2 - 5x - 6 = 0
• x^3 - 2x^2 + 4x^2 - 8x +3x - 6 =
• (x - 2)(x^2 + 4x + 3) =
• (x - 2)(x^2 + x + 3x + 3) =
• (x - 2)(x(x + 1) + 3(x + 3)) =
• (x - 2)(x + 1)(x + 3)

Zero's are

• x = 2, x = -1, x = -3

See the graph attached

Correct end behavior as per graph:

• As x approaches negative infinity, f(x) approaches negative infinity