Presentation on theme: "Zeros and End Behavior Objective: Be able to find zeros and end behavior of a graph. TS: Making decisions after reflection and review."— Presentation transcript:
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.
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)
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!