Unit+6+Journal

__ ** Unit 6: Polynomial Functions ** __

**__ 6.1: __**
For each of the groups below, identify the graph that does not belong and state your reasoning why that graph does not belong in your online journal.

Group 1- the first graph doesn't belong, because it's not a polynomial function. Group 2- the second graph doesn't belong because it's not a polynomial function. Group 3- the third graph doesn't belong, because it's not a polynomial function. Group 4- the third graph doesn't belong, because it's not a polynomial function.These four graphs are linear.
 * Answer the following questions in your online journal: **
 * Based on the examples above, explain how you can determine the end behavior of a function when your are only given an equation.
 * In group 2, identify the number of roots each function. Using these three examples, explain how you can predict the number of roots when only given the equation.
 * When you're only given an equation, you can determine the end behavior by looking at the degree and leading coefficient.
 * The first function has only one x-intercept. The second function also has one x-intercept. The third function has 4 x-intercepts. You can predict the number of roots when only given the equation by looking at the end bahavior.

__** 6.2: **__
Summarize the last two days of class in your online journal. We have discussed different methods for graphing polynomial functions in intercept form. In detail, explain the graphing method to a student who has missed the last two days.

When graphing a polynomial function in intercept form, a very important thing to consider is the end behavior. The end behavior is determined by the degree and leading coefficient. The degree and leading coefficient gives you an idea of how your graph is going to look. Also, you need to look and see how many times the factors are repeated. This will tell you whether the line will touch or cross the the x-axis.

__** 6.3: **__
Watch the video below to complete the worksheet handed out in class. The examples on the handout are the same as the examples in the video, so complete the example along with the video. After completing the examples, do the practice problems on the handout as well. Be sure to complete the summary at the bottom of the handout.

__** 6.4: **__
In your online journal, reflect upon your performance and experience so far this year in Algebra 2 CP. Discuss your work ethic, effort, attitude and motivation. What are your goals for the rest of the a year? What do you need to do to be sure you reach your goal before the year is done? Based on what you have done so far and how you plan on improving the rest of the year, make a goal for your final grade for the year. Be sure this goal is a number grade, not just a letter grade.

- So far this year in Algebra 2 CP, I've learned many new concepts. I feel like i have been able to comprehend these concepts and perform well in the class. Things that i can improve on is my work ethic and effort. I'm perfectly capable of doing the work, I'm just lazy. My goals for the rest of the year is to complete every single homework assignment. I feel like if i had done my homework more consistently, my grades would've been better in the recent quarters. By the end of the year, i want to have a final grade of 88.

__** 6.5: **__
On the handout from class, answer the questions as you watch the video. Once the video is complete, use the new method to complete the handout and the problem from the video.

__** 6.6: **__
Listed below are 6 graphs and 12 equations. Some equations are written in intercept form, and some in standard form. A single graph will match one of each type of equation. (2 equations per graph.)

In your online journal, explain your thought process and order of matching the equations and graphs together.
 * For example t(x) and u(x) match graph 7 because ... **
 * What properties did you look at first? What types of equation did you match first?
 * What type of equation was the hardest to match?
 * How did you narrow down your choices?

[|Wikispace 6.6.doc]

a(x) and u(x) match graph 6 because they both have and even degree and negative leading coefficient. Also, a(x) has x-intercepts at (x+2), (x-2), (x-1), (x-5)

p(x), p(x) and L(x) match graph 5, because they both have an even degree and negative leading coefficient. Also because, p(x) has x-intercepts at (x+1) (x-1), (x+3), and (x-2)

n(x) and i(x) match graph 4, because they both have an even degree and positive leading coefficient. They're both up on the left and up on the right.

__** 6.7: **__

 * The average height (in inches) for boys ages 1 to 20 can be modeled by the function B(x) = -0.001x^4 + 0.04x^3 - 0.56x^2 + 5.5x +25, where x is the age (in years). **


 * The average height (in inches) for girls ages 1 to 20 can be modeled by the function G(x) = 0.00007x^4 - 0.00276x^3 - 0.012x^2 + 3.1x + 27, where x is the age (in years). **

Use the link below to graph both functions then answer the following questions in your online journal. [|Graphing Tool]


 * What is the domain of both these function and explain why this domain is appropriate according to the context of the situation.
 * What is an appropriate range for each function. Explain why this range is appropriate according to the context of the situation.
 * Find B(7) and G(9). Write what this means in the context of the situation.
 * What year is the average height for boys the greatest?
 * What is the highest average height for the girls?
 * Describe the shape of the graphs. Why is this shape appropriate according to the context of the situation? Could you use this model to predict the height of a male at the age of 45? Explain.