Question

NEED HELPPPPPPP!!!!!!! PLEASE!!!!!!!!

Which statement best describes the graph of -x3 - x2 + 4x + 4?

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

B.It starts down on the left and goes up on the right and intersects the axis at x = -2, -1, and 2.

C.It starts up on the left and goes down on the right and intersects the x-axis at x = -2, -1, and 2.

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

Answer 1

Firstly, simplife the function $-x^3-x^2+4x+4$ in the following way:

$-x^3-x^2+4x+4=-(x^3+x^2)+4(x+1)=-x^2(x+1)+4(x+1)=(x+1)(4-x^2)=(x+1)(2-x)(2+x)=-(x+2)(x+1)(x-2)$.

There are three x-intercepts: x=-1; x=2 and x=-2 (therefore, options A and D are incorrect).

Since before brackets is sign "-", you should state that graph starts down on the left (you can check this substituting smaller negative number than -2 into function expression. For example, if x=-10, then f(-10)=-(-10+2)(-10+1)(-10-2)=-(-8)(-9)(-12)>0) and goes up on the right (you can check this substituting greater positive number than 2 into function expression. For example, if x=10, then f(-10)=-(10+2)(10+1)(10-2)=-(12)(11)(8)<0).

Answer: correct choice is B.