Warm Up: Solve & Sketch the graph:. Graphing Polynomials & Finding a Polynomial Function.

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Warm Up: Solve & Sketch the graph:

Graphing Polynomials & Finding a Polynomial Function

Equivalent Statements: x = a is a zero of the function f. x = a is a solution of the polynomial equation f(x)=0. (x-a) is a factor of the polynomial f(x) (a, 0) is an x-intercept of the graph of f

Multiplicity

Repeated Zeros

Sketch the graph: Multiplicity of 2. Touches. Through these Points. End behavior:

Multiplicity - repeated zero – Means………….. If it occurs an odd number of times, the graph crosses the x-axis at the zero. If it occurs an even number of times, the graph will just touch the x-axis at the zero.

Sketch the graph: Mult. of 3 Goes Through Mult. Of 2 Touches 1 st Term would be End Behavior: 13 xy

Sketch the graph: Both have a multiplicity of 2. Just Touch! xy 1 st Term would be End Behavior:

Can you write a polynomial function if you know the zeros?

Find a Polynomial function that has the given zeros: 6, -3

Find a Polynomial function that has the given zeros: 0, 3, -5

Find a Polynomial function that has the given zeros: 3, 2, -2, -1

Find a Polynomial function that has the given zeros: and

Long & Synthetic Division

Use Long Division and use the result to factor the polynomial completely. 1 st Step:

2 nd Step:

Divide using long division: Remainder

Divide using long division:

You Try: Divide using long division

Divide using long division

Synthetic Division

Divide using synthetic division to find the zeros:

Divide using synthetic division:

You Try: Divide using synthetic division – Find zeros: 4

You Try: Divide using synthetic division: