Answer
$\mathrm{x} = \text{–}5$ has multiplicity 1 (odd)
The graph crosses the x-axis.
$\mathrm{x} = -2$ has multiplicity 2 (even)
The graph touches the x-axis and turns around.
Work Step by Step
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 $r$.
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Zeros: $-5$ and $-2.$
$\mathrm{x} = \text{–}5$ has multiplicity 1 (odd)
The graph crosses the x-axis.
$\mathrm{x} = -2$ has multiplicity 2 (even)
The graph touches the x-axis and turns around.
