Pre-Calculus 12 Notes

By: Gen L.

Lesson 6: Characteristics of Polynomials

What is a Polynomial?

A function in the form ,
where

Examples:

Terminology

The Degree of is the greatest power of

The Lead Coefficient of is the coefficient of

Characteristics of Polynomials

• Lead Coefficient:
• Degree: same direction. opposite direction.
• Degree Value: min directions and min roots.
• -intercept:
• Domain: or
• Range: , based on relative extrema.

Polynomials:

• Constant:
• Linear:
• Quadratic:
• Cubic:
• Quartic:
• Quintic:
• Roots: no. of roots
• Turns: no. of turns

Descriptions

Describe the characteristics of

• LC: Right end behaviour:
• Deg: Left end behaviour:
• At most 4 turns & 5 roots & directions
• -int:
• Domain:
• Range:

Range Determination

For determine the range.

• LC: Right end behaviour:
• Deg: Left end behaviour:
• -int: (0, -5)
• Range:

You'll likely find this by graphing. If you decide to continue on this path to Calculus, you learn how to actually calculate this.

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