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Slide 1

Functions

Dr. Claude S. Moore Danville Community College

PRECALCULUS I

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## Polynomial Function

A polynomial function of degree n is where the a’s are real numbers and the n’s are nonnegative integers and an  0.

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A polynomial function of degree 2 is called a quadratic function.

It is of the form a, b, and c are real numbers and a  0.

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## Axis of Symmetry

For a quadratic function of the form gives the axis of symmetry.

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## Standard Form

A quadratic function of the form is in standard form.

axis of symmetry: x = h vertex: (h, k)

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## Characteristics of Parabola

a > 0

a < 0

vertex: minimum

vertex: maximum

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Higher Degree Polynomial Functions

Dr. Claude S. Moore Danville Community College

PRECALCULUS I

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## Characteristics

The graph of a polynomial function…

1. Is continuous.

2. Has smooth, rounded turns.

3. For n even, both sides go same way.

4. For n odd, sides go opposite way.

5. For a > 0, right side goes up.

6. For a < 0, right side goes down.

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.

an < 0

graphs of a polynomial function for n odd:

an > 0

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.

an < 0

graphs of a polynomial function for n even:

an > 0

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## Roots, Zeros, Solutions

The following statements are equivalent for

real number a and polynomial function f :

1. x = a is root or zero of f.

2. x = a is solution of f (x) = 0.

3. (x - a) is factor of f (x).

4. (a, 0) is x-intercept of graph of f (x).

Slide 12

1. If a polynomial function contains a factor (x - a)k, then x = a is a repeated root of multiplicity k.

2. If k is even, the graph touches (not crosses) the x-axis at x = a.

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