Honors Pre-Calculus A, 4th Hour, Winter 2015: POLYNOMIAL FUNCTIONS & COMPLETEING THE SQUARE

Polynomial Functions

DEFINED AS...

A polynomial function is of the form: This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

- the value of This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

must be a nonnegative integer (meaning it is a whole number and is equal to zero or is a positive integer-- no fractions or radicals!)
- all coefficients ( This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

) have to be real numbers
- the degree of the polynomial is the highest value of This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

where

- is continuous
- has a domain of all real numbers
EXAMPLE
This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

Completing the Square

Completing the square involves taking a polynomial and rewriting it in standard form.

Standard form of a quadratic is

For EXAMPLE... This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

To rewrite this polynomial function in standard form, we will visualize the terms of the polynomial as squares.

We need one box of This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

, 6 boxes of This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.

, and 8 boxes of 1.