1. 10/19
Staple pages 244,245,249,250,255 together. Put your name on it.
To begin class, complete the following with a partner. We will answer a total of 10 questions here, so pencil/paper!
1. What is a “zero” or “root”? Our textbook uses these words synonymously.
Are they all x-intercepts? If some zeros are not x-intercepts, how can we describe them?
2. The Fundamental Theorem of Algebra (FTA) tells us what about the relationship between the number of zeros and degree?
3. Sketch a linear function (where the slope is anything but zero). What is the degree of a linear function? How many roots/zeros will it have? Is it real?

2. Now, sketch a quadratic function. Compare yours with your partner’s.
Based on the FTA, how many zeros does a quadratic function have? How many does your and your partner’s graph have?
Can you draw a different quadratic function that has different combinations of real and imaginary roots? Compare yours to your partner’s again.
There are 3 different cases for quadratic functions in terms of the types of zeros. Can you sketch all 3? Discuss this with your partner.

3. So, do your graphs look something like these?
Notice, the textbook calls zeros with a multiplicity of 1 “distinct.”

And bounces “1 real (multiplicity of 2)”
And, of course, if the zeros aren’t x- intercepts, they are imaginary.

4. Cubic Functions
There are four cases for cubic functions in regards to the types and number of zeros. Of course, cubic functions are degree 3 poly’s. Which means they’ll have different combinations of zeros, but always how many total?
Attempt to identify and sketch all four cases for cubic functions! Work and check with your partner for help identifying all four cases.

5. It’s important to remember that imaginary zeros ALWAYS come in pairs, so a cubic function can have 2 imaginary zeros, but the other must be real.
10. Does a cubic function always have at least 1 real root? Why? Is this true for all odd degree polynomials?

6. 4th degree (quartic) and 5th degree (quintic) polynomials
Let’s look at pages 247 and 248 from the textbook. Attempt, with your partner, to sketch all cases for 4th and 5th degree polynomials!