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 2 ; lies below the $x$-axis between 0 and 2 .
A) $f ( x ) = x ^ { 3 } - 2 x ^ { 2 }$
B) $f ( x ) = x ^ { 3 } + 2 x ^ { 2 }$
C) $f ( x ) = - x ^ { 3 } + 2 x ^ { 2 }$
D) $f ( x ) = - x ^ { 3 } - 2 x ^ { 2 }$

Question

Quizplus · Accepted Answer

The zeros of the polynomial $f(x) = x^3 - 2x^2$ are $x = 0$ and $x = 2$. The zero at $x = 0$ has a multiplicity of 1, indicating the graph crosses the x-axis at this point. The zero at $x = 2$ also has a multiplicity of 1, meaning the graph crosses the x-axis at this point as well. The description of the graph lying below the x-axis between 0 and 2 matches the behavior of this polynomial function.

Find the Zeros for the Polynomial Function and Give the Multiplicity