Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses
the x-axis or touches the x-axis and turns around, at each zero.
-Touches the $x$-axis at 0 and crosses the $x$-axis at 4 ; lies above the $x$-axis between 0 and 4 .
A) $f ( x ) = - x ^ { 3 } + 4 x ^ { 2 }$
B) $f ( x ) = x ^ { 3 } + 4 x ^ { 2 }$
C) $f ( x ) = x ^ { 3 } - 4 x ^ { 2 }$
D) $f ( x ) = - x ^ { 3 } - 4 x ^ { 2 }$

Question

Quizplus · Accepted Answer

The polynomial $f(x) = -x^3 + 4x^2$ has zeros at $x = 0$ and $x = 4$. The zero at $x = 0$ has a multiplicity of 2, indicating the graph touches the x-axis and turns around at this point. The zero at $x = 4$ has a multiplicity of 1, meaning the graph crosses the x-axis at this point. The negative leading coefficient indicates the graph lies above the x-axis between these zeros before turning downward.

Find the Zeros for the Polynomial Function and Give the Multiplicity