Pre-Calculus 12 Notes

By: Gen L.

Lesson 7: Graphing Polynomials

"Graphing"

When I say graphing, unless you're using an actual graphing calculator, you only need to make a sketch.

Factoring Expressions

Factor

Graphing

Graph

• LC:
• Deg:
• max 4 directions, 3 turns, 4 roots
• -int:
• -int:
• Try graphing this in Desmos. What do you notice?

Multiplicity

For a zero:

• if will bounce.
• if and will cross -axis straight.
• if and will cross -axis curved.

Graphing Factored Expressions

Graph

• LC:
• Deg:
• max 4 directions, 3 turns, 4 roots
• -int:
• -int:

Determining Equations

Determine an equation for a polynomial, with roots at 3 and -2 (), and passes through the point .

• Roots:
• Point:
  
• Find

To find , we disregard , and plug in , and divide by that value.

We get .

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