1 / 12

Zeros and End Behavior

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

kana
Download Presentation

Zeros and End Behavior

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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: • 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. • 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. y = x2 + 2x + 1 • y =-2x2 + 3x – 1 • y = -x2 • y = 2x2 – 1 e) y = 2x3 + 4x – 1 • y = -x3 + 2x – 1 • y = 4x4 + 1 • y = 3x3 – 2 • y = 5x5 • y = -4x5 + 1 • y = 8x8 • y = -4x7 + 5x3 – 4x – 1 • y = 8x3 – 4x4 – 2x + 3 • y = -3x5 + 4x6 – x4

  4. End Behavior Right Hand Side Left Hand Side

  5. Find the zeros of each of the following. • y = x3 + x2 – x – 1 • y = x4 – 8x2 + 16 • y = 2x5 + x4 – 6x3 • y = -2(x + 2)2(x – 2) • 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… • Find the end behavior • Find the zeros and their multiplicities • Find the y-intercept • Sketch away!

  8. Sketch • y = x3 + x2 – x – 1

  9. Sketch 2) y = x4 – 8x2 + 16

  10. Sketch 3) y = 2x5 + x4 – 6x3

  11. Sketch 4) y = -2(x + 2)2(x – 2)

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

More Related