In all the problems do the following:

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In all the problems do the following: Starter – Day 4 November 4 Content Objective: We will work with and analyze complex zeros. *Complex numbers have real parts and imaginary parts. In all the problems do the following: Find the zeros (you might have to factor first) List the multiplicity of each zero Does the graph touch or cross at each zero Describe left/right end behavior Find a power function that is an end behavior asymptote Sketch the graph. Zero Multiplicity Touch/Cross? Left End Behavior Right End Behavior Power Function E.B.A. X intercept(s) Y intercept

LAB Writing Explain in writing what the y-intercept and x-intercepts of a graph are.

Complex Zeros: Conjugate Pairs 3i, -3i 2+5i, 2-5i 9i 3, 1-7i

Complex Zeros: How many real roots? Total # of Zeros Possible # Real Possible # Imaginary Total # of Zeros Possible # Real Possible # Imaginary Total # of Zeros Possible # Real Possible # Imaginary

Rational Roots Constant Factors Leading Coefficient Factors Possible Rational Roots Constant Factors Leading Coefficient Factors Possible Rational Roots Constant Factors Leading Coefficient Factors Possible Rational Roots

Descarte’s Rule of Sign # positive real zeros: # negative real zeros: # positive real zeros: # negative real zeros: # positive real zeros: # negative real zeros:

Intermediate Value Theorem If there is a polynomial with points (2,1) and (4, -3), is there at least one zero between x=2 and x=4? If f(x) is a polynomial function with f(2)=1 and f(4)= -3, is there at least one zero of f(x) between x=2 and x=4?

Intermediate Value Theorem If f(x) is a polynomial function with f(-6)=7 and f(-1)= 1, would it be safe to say that f(x) must be equal to 4 somewhere between -6 and -1? If f(x) is a polynomial function with f(-4)=5 and f(1)= -4, is there at least one zero of f(x) between x=-4 and x=1?

Remainder Theorem If , what is the remainder when you divide by ? What is the value of ?

Find all Complex Zeros: Three different ways