Find the x- and y-intercepts for the function defined by y = f (x). $$f ( x ) = ( x - 1 ) ( x + 4 ) ( x + 5 ) ^ { 2 }$$
A) $x$-intercepts: $( 1,0 ) , ( - 4,0 ) , ( - 5,0 ) ; y$-intercept: none
B) $x$-intercepts: $( - 1,0 ) , ( 4,0 ) , ( 5,0 ) ; y$-intercept: none
C) $x$-intercepts: $( - 1,0 ) , ( 4,0 ) , ( 5,0 ) ; y$-intercept: $( 0 , - 100 )$
D) $x$-intercepts: $( 1,0 ) , ( - 4,0 ) , ( - 5,0 ) ; y$-intercept: $( 0 , - 100 )$

Question

Quizplus · Accepted Answer

The x-intercepts are found by setting $y = 0$ and solving for $x$, which gives the roots $x = 1$, $x = -4$, and $x = -5$. The y-intercept is found by setting $x = 0$ in the function, resulting in $y = (0 - 1)(0 + 4)(0 + 5)^2 = -100$.

Find the X- and Y-Intercepts for the Function Defined by Y