Question

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

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

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

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

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

Answer 1

please help me...

Answer 2

\[\begin{align*}-x^3-x^2+4x+4&=-x^2(x+1)+4(x+1)\\&=(4-x)^2(x+1)\end{align*}\]
So you know the zeroes of the polynomial are \(x=-1,4\).

To figure out the behavior of the polynomial around these zeroes, pick a value from the spaces between the zeroes and plug them in.