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.
-$$f ( x ) = - x ^ { 3 } ( x + 4 ) ^ { 2 } ( x - 7 )$$
A) 0 , crosses the $x$-axis;
$- 4$, touches the $x$-axis and turns around;
7 , crosses the $x$-axis
B) 0 , crosses the $x$-axis;
4 , touches the $x$-axis and turns around;
$- 7$, crosses the $x$-axis
C) 0 , touches the $x$-axis and turns around;
$- 4$, touches the $x$-axis and turns around;
7 , crosses the $x$-axis
D) 0 , touches the $x$-axis and turns around;
4 , crosses the $x$-axis;
7 , crosses the $x$-axis

Question

Quizplus · Accepted Answer

The x-intercepts are found by setting the function equal to zero and solving for x, which gives $x = 0$, $x = -4$, and $x = 7$. The exponent of $x^3$ indicates the graph crosses the x-axis at $x = 0$. The squared term $(x + 4)^2$ indicates the graph touches the x-axis and turns around at $x = -4$. The linear term $(x - 7)$ indicates the graph crosses the x-axis at $x = 7$.

Find the X-Intercepts of the Polynomial Function f(x)=−x3(x+4)2(x−7)f ( x ) = - x ^ { 3 } ( x + 4 ) ^ { 2 } ( x - 7 )f(x)=−x3(x+4)2(x−7)

Find the X-Intercepts of the Polynomial Function $f ( x ) = - x ^ { 3 } ( x + 4 ) ^ { 2 } ( x - 7 )$