Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.
-$$f ( x ) = ( x + 1 ) ( x - 9 ) ( x - 1 ) ^ { 2 }$$
A) $- 1$, crosses the $x$-axis;
9 , crosses the $x$-axis;
1 , touches the $x$-axis and turns around
B) $- 1$, crosses the $x$-axis;
9 , crosses the $x$-axis;
1 , crosses the $x$-axis
C) 1 , crosses the x-axis;
$- 9$, crosses the $x$-axis;
$- 1$, touches the $x$-axis and turns around
D) 1 , crosses the x-axis;
$- 9$, touches the $x$-axis and turns around;
$- 1$, touches the $x$-axis and turns around

Question

Quizplus · Accepted Answer

The x-intercepts are found by setting $f(x) = 0$, which gives $x = -1$, $x = 9$, and $x = 1$. The graph crosses the x-axis at $x = -1$ and $x = 9$ because these factors are to the first power. It touches and turns around at $x = 1$ because this factor is squared, indicating a multiplicity of 2.

Find the X-Intercepts of the Polynomial Function f(x)=(x+1)(x−9)(x−1)2f ( x ) = ( x + 1 ) ( x - 9 ) ( x - 1 ) ^ { 2 }f(x)=(x+1)(x−9)(x−1)2

Find the X-Intercepts of the Polynomial Function $f ( x ) = ( x + 1 ) ( x - 9 ) ( x - 1 ) ^ { 2 }$