Question

(25 points)

Which statement best describes the graph of x^3 - 3x^2 - 4x + 12?

It starts down on the left and goes up on the right and intersects the x-axis at x = -2, 2, and 3.
It starts down on the left and goes up on the right and intersects the axis at x = -2, 4, and 3.
It starts up on the left and goes down on the right and intersects the axis at x = -2, 2, and 3.
It starts up on the left and goes down on the right and intersects the axis at x = -2, 4, and 3.

Answer 1

x³ - 3x² - 4x + 12=(x³ - 3x²) - (4x - 12)=x²(x-3)-4(x-3)= (x-3)(x²-4)=(x-3)(x-2)(x+2)
equation cross x-axis in point x=-2, x=2, x=3
so we can choise from 1 and 3 answers:
It starts down on the left and goes up on the right and intersects the x-axis at x = -2, 2, and 3.
It starts up on the left and goes down on the right and intersects the axis at x = -2, 2, and 3.

coefficient before x³>0 so it go up
so it ís answer 1
Answer:
1. It starts down on the left and goes up on the right and intersects the x-axis at x = -2, 2, and 3

Answer 2

The answer is A.

The 0's of the function are -2, 2, and 3.

The graph starts from the bottom left and it keeps going to the top right.