Notes on graphing polynomials.notebook

1

January 23, 2018

Notes on graphing polynomials.notebook

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January 23, 2018

How to Graph a Polynomial Function1. Find the real zeros (x­intercepts where y=0)

Factor it:

• GCF (Always check first)

• Guess and check (double bubble for quadratic trinomials)

• By grouping (4 terms)

• Complete the square (quadratic trinomial)

• Quadratic Formula (quadratic trinomial)

• RRT (p’s and q’s) (4 or more terms)

2. Find the y­intercepts

Set x = 0

3. Need heights

Find at least 2 points between each zero using a table

4. End behavior

5. Plot and connect with smooth curves

Find maximum/minimum values using your calculator

Notes on graphing polynomials.notebook

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January 23, 2018

Ex. 3 Graph the function f(x) = x3 + 3x2 ­ 6x ­ 8

1. Find/graph the x­intercepts by setting = 0 

and solving

2. Find the max/min values on your calculator 

and graph them

3. Connect in a smooth curve making sure

to pay attention to end behavior

Notes on graphing polynomials.notebook

4

January 23, 2018

Graph f(x) = x3 ­ 2x2 ­ 5x + 6

Notes on graphing polynomials.notebook

5

January 23, 2018

Notes on graphing polynomials.notebook

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January 23, 2018

Ex. 5  A welder plans to construct an open box from a single piece of sheet metal 18.5' x 24.5' by cutting squares from the corners and folding up the sides.  What is the box's maximum volume?

24.5

18.5

x

x

x

x

x

x

x x