Find the x- and y-intercepts of f.
-$$f ( x ) = - x ^ { 2 } ( x + 4 ) \left( x ^ { 2 } + 1 \right)$$
A) $x$-intercepts: $- 4 , - 1,0,1$; y-intercept: 0
B) $x$-intercepts: $- 4,0 ; y$-intercept: 0
C) $x$-intercepts: $- 4 , - 1,0 ; y$-intercept: 4
D) $x$-intercepts: $- 4 , - 1,0$; y-intercept: $- 4$

Question

Quizplus · Accepted Answer

To find the x-intercepts, set $f(x) = 0$. The equation becomes $-x^2(x + 4)(x^2 + 1) = 0$. The solutions are $x = 0$ and $x = -4$; $x^2 + 1 = 0$ has no real solutions because $x^2 + 1 > 0$ for all real x. For the y-intercept, set $x = 0$, which gives $f(0) = 0$.

Find the X- and Y-Intercepts of F f(x)=−x2(x+4)(x2+1)f ( x ) = - x ^ { 2 } ( x + 4 ) \left( x ^ { 2 } + 1 \right)f(x)=−x2(x+4)(x2+1)

Find the X- and Y-Intercepts of F $f ( x ) = - x ^ { 2 } ( x + 4 ) \left( x ^ { 2 } + 1 \right)$