Download presentation

Presentation is loading. Please wait.

Published byJohnathan Stanford Modified over 2 years ago

1
Zeros and End Behavior Objective: Be able to find zeros and end behavior of a graph. TS: Making decisions after reflection and review

2
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.

3
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 4 + 1 h)y = 3x 3 – 2 i)y = 5x 5 j)y = -4x 5 + 1 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

4
End Behavior Right Hand Side Left Hand Side

5
Find the zeros of each of the following. 1)y = x 3 + x 2 – x – 1 2)y = x 4 – 8x 2 + 16 3)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)

6
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?..

7
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!

8
Sketch 1)y = x 3 + x 2 – x – 1

9
Sketch 2) y = x 4 – 8x 2 + 16

10
Sketch 3) y = 2x 5 + x 4 – 6x 3

11
Sketch 4) y = -2(x + 2) 2 (x – 2)

12
Sketch 5) y = 3(x – 1) 3 (x + 2) 2 (x – 4)

Similar presentations

OK

Graphs of Equations Objectives: Be able to find solutions, intercepts and the symmetry of a graph by hand and by using the calculator. TS: Analyzing.

Graphs of Equations Objectives: Be able to find solutions, intercepts and the symmetry of a graph by hand and by using the calculator. TS: Analyzing.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on computer malware scanner Ppt on market friendly state Ppt on ideal gas law constant Ppt on hiroshima and nagasaki attacks Ppt on advertisement of honda city Ppt on bluetooth based smart sensor networks Ppt on forward rate agreement calculator Ppt on email etiquettes presentation tips Ppt on transportation and excretion in human body Ppt on cell the basic unit of life