Precalc algebra 2

Real roots

1. Real number solutions to the equation f(x)=0 {simply, the x-intercepts}

2. The graph of f(x) crosses or bounces off the x-axis at these x-values

Root form

Factored form of the polynomial

Multiplicity

The number of times a root appears in the list of roots

• example: (x-2)(x-2)=(x-2)²

  • x=2 has a multiplicity of 2

• Find after finding real root, illustrated in the example above

Odd

The graph of a polynomial function crosses the x-axis at a real root if the multiplicity of the root is

Even

The graph touches (bounces off) but does not pass through the x-axis if the multiplicity of the root is

Exponent

In the factored form, the multiplicity can be seen as this on the factor

Flattening

As the multiplicity increases, the graph of the polynomial remains close to the x axis. This can be seen as