Question

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

Answer 1

for $f(x)=ax^n+bx^{n-1}...+z$ where n is the highest power of the function
if n is even and 'a' is positive, the graph goes from top left to top right
if n is even and 'a' is negative, the graph goes from bottom left to bottom right      
if n is odd and 'a' is positive, the graph goes from bottom left to top right           
if n is odd and 'a' is negative, the graph goes from top left to bottom right


and, for $f(x)=a(x-r_1)(x-r_2)(x-r_3)...(x-r_n)$, it intersects the graph at $x=r_1$, $x=r_2$,$x=r_3$, up to $x=r_n$,

so see what we've got$f(x)=-x^3-x^2+4x+4$            
factor and group              
$-x^3-x^2+4x+4=(-x^3-x^2)+(4x+4)=$                 $(-x^2)(x+1)+(4)(x+1)=(x+1)(4-x^2)=(x+1)(2-x)(2+x)=$                $-1(x+2)(x+1)(x-2)$                     $f(x)=-1(x-(-2))(x-(-1))(x-2)$                a=-1               the roots are x=-2, x=-1, x=2                since n=3 (from $-x^3-x^2+4x+4$) and a is negative, we know it goes from top left to bottom right             also, it intersects at x=-2,-1, and 2

answer is the 3rd option: It starts up on the left and goes down on the right and intersects the x-axis at x = −2, −1, and 2.