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.
-$$f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 6 )$$
A) 0 , touches the $x$-axis and turns around;
5 , crosses the $x$-axis;
6 , crosses the $x$-axis
B) 0 , touches the $x$-axis and turns around;
$- 5$, crosses the $x$-axis;
$- 6$, crosses the $x$-axis
C) 0 , crosses the $x$-axis;
5 , touches the $x$-axis and turns around;
6 , touches the $x$-axis and turns around
D) 0 , crosses the $x$-axis;
5 , crosses the $x$-axis;
6 , crosses the $x$-axis

Question

Quizplus · Accepted Answer

The x-intercepts are found by setting $f(x) = 0$, which gives $x = 0$, $x = 5$, and $x = 6$. The factor $x^2$ indicates that at $x = 0$, the graph touches the x-axis and turns around (because the power is even), while at $x = 5$ and $x = 6$, the graph crosses the x-axis (because the powers are odd).

Find the X-Intercepts of the Polynomial Function f(x)=x2(x−5)(x−6)f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 6 )f(x)=x2(x−5)(x−6)

Find the X-Intercepts of the Polynomial Function $f ( x ) = x ^ { 2 } ( x - 5 ) ( x - 6 )$