Zeros and End Behavior Objective: Be able to find zeros and end behavior of a graph. TS: Making decisions after reflection and review

Exploration: a)Find the end behavior of each of the following equations. Look for a pattern and then describe how you would find the end behavior without actually graphing. b)Find the number of x-intercepts of each of the equation. See if you can find a connection between the number of x-intercepts and the equation itself.

a)y = x 2 + 2x + 1 b)y =-2x 2 + 3x – 1 c)y = -x 2 d)y = 2x 2 – 1 e) y = 2x 3 + 4x – 1 f)y = -x 3 + 2x – 1 g)y = 4x h)y = 3x 3 – 2 i)y = 5x 5 j)y = -4x k)y = 8x 8 l)y = -4x 7 + 5x 3 – 4x – 1 m)y = 8x 3 – 4x 4 – 2x + 3 n)y = -3x 5 + 4x 6 – x 4

End Behavior Right Hand Side Left Hand Side

Find the zeros of each of the following. 1)y = x 3 + x 2 – x – 1 2)y = x 4 – 8x )y = 2x 5 + x 4 – 6x 3 4)y = -2(x + 2) 2 (x – 2) 5)y = 3(x – 1) 3 (x + 2) 2 (x – 4)

Multiplicity When a zero is repeated it is said to have a multiplicity equal to degree of it’s factor. Which zeros from the last examples have a multiplicity, and what are their multiplicites? What happens to the graph when a zero has a multiplicity?..

Graph sketching When you’re asked to sketch a graph… 1)Find the end behavior 2)Find the zeros and their multiplicities 3)Find the y-intercept 4)Sketch away!

Sketch 1)y = x 3 + x 2 – x – 1

Sketch 2) y = x 4 – 8x

Sketch 3) y = 2x 5 + x 4 – 6x 3

Sketch 4) y = -2(x + 2) 2 (x – 2)

Sketch 5) y = 3(x – 1) 3 (x + 2) 2 (x – 4)