## College Algebra (6th Edition)

$x = 0$ has multiplicity 1 (odd). The graph crosses the x-axis. $x = -2$ has multiplicity $2$ (even). The graph touches the x-axis and turns around.
Multiplicity and x-Intercepts: If $r$ is a zero of a polynomial f(x), then $(x-r)^{k}$ is a factor in the full factorization of f. The exponent $k$ indicates the multiplicity of $r$. If $r$ is a zero of even multiplicity, then the graph touches the x-axis and turns around at $r$. If $r$ is a zero of odd multiplicity, then the graph crosses the x-axis at $r$. ------------------ Begin factoring by factoring x out of the expression for f(x) $f(x)=x(x^{2}+4x+4)$ ... recognize a square of a sum... $f(x)=x(x+2)^{2}$ Zeros: $0$ and $-2.$ $x = 0$ has multiplicity 1 (odd). The graph crosses the x-axis. $x = -2$ has multiplicity $2$ (even). The graph touches the x-axis and turns around.