Warm Up

Polynomial Graphs

March 17th & 18th, 2014

The functions we will look at…

What you will need to know…

Important Terminology

Polynomial Functions

Max/Min Points – Turning PointsUse calculator to find…

Zero

Cubic Polynomials

Investigating Transformations

Graphing Cubic Polynomials

Example

Example

Graphing Quartic Polynomials

Example

Example

End Behavior SummaryDegree Positive

Leading Coefficient

Negative Leading Coefficient

Even

Odd

Does the zero cut or touch?

If the exponent is EVEN the zero TOUCHES

If the exponent is ODD the zero CUTS (goes through)

Examples

Example

• Sketch the graph of the equation y = -x(x-1)2

Example

• Sketch the graph of the equation f(x) = (x + 1)(x – 2)(x – 4)

Example

• Sketch the graph of the equation y = -(x + 3)(x + 2)(x – 1)3

Example• Sketch the graph of the equation with a double root at

–2, a single root at 5, a triple root at 0 and a double root at 2. Assume the leading coefficient is negative one. Write the equation of the function that describes the graph.

Example• Write the equation for the polynomial graph shown.

Assume that all even multiplicities are 2 and all odd multiplicities are 3

Finish the worksheet

• Sketch the functions!

Classwork• Complete the worksheet #1-8• Sketch the Graph• Find the zeros• Find the relative max & mins• State the number of turning points• State the END BEHAVIOR

Homework

A Day Edition 2• Finish Kuta Software

Worksheet• Pg. 671 #1• Pg. 672 #2, 3, 4

B Day Edition 1• Finish Kuta Software

Worksheet• Pg. 549 #1 g,h,i , #2 c• Pg.550 #1• Pg. 552 #2• Pg. 555 #1 A-D• Pg. 556 #3