Unit+6+Journal

6.1 In group 1, the first doesn't belong because it's a straight line. In group 2 the second doesn't belong because it's negative, in group 3 the first doesn't belong because it's positive, and in group 4 the third doesn't belong because it's negative. > You can determine the end behavior by whether the Q is positive or negative, and by whether the P is even or odd. > f(x) has ? root(s), g(x) has ? root(s), and k(x) has ? root(s). You can predict the number of roots when only given an equation by ???. 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. To graph polynomial functions you need to look at the LC and the highest exponent (I forget what this is called, so for now it's HE). If the LC is positive and the HE is even, then it'll be a "U" shape. If the LC is negative and the HE is even, then it will be an upside-down "U" shape. If the LC is negative and the HE is odd, then the left side will be down, and the right side will be up. If the LC is positive and the HE is odd, then the left side will be down and the right side will be up. If you have difficulty remembering which squiggle is positive and which is negative, connect the ends with a straight line, and it will slant negative or positive, then you can tell if it's the right one. :D
 * 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.

6.3 Talk about how to use synthetic substitution to evaluate a polynomial functions and find its factors. When you use synthetic substitution to evaluate a polynomial and find it's factors you first take the P (Which is the number without an X, etc) and list all the numbers that go into it. So, for example, if the P is 8, you'd write down +/- {1,8,2 and 4}. Then you do the same for the Q (which is the LC.). When you get all of the numbers, you put the Ps over the Qs to get your possible factors. So, if like in the example above my P was 8 and my Q was, say 1, my possible factors would be +/- {1/1, 8/1, 2/1, and 4/1}; or +/- {1, 8, 2, and 4}. Remember that you have to write the +/- so you don't forget that either of them could be a factor. After you have all of your possible factors (PFs) you plug each of them into a synthetic substitution problem, where the PF goes into the left top box, the coefficients go into the top of the middle long box, and the right bottom box is space for what hopefully ends up in a 0. To find this out you put the PF in the bottom of the middle box, under the first coefficient number. You add those two and put that number under them outside of the box. You take the sum of those two and multiply it by the PF. You take the product of that and put it into the next space under the second coefficient. You keep doing this for all of the coefficients, and when you get to the last one it can either = 0, making it a factor, or it can = a number, which would make it a point on the graph. *NOTE: If an exponent is skipped, you put a 0 in its place in the line, so say the function goes: f(x)=5x^4+ 4x^3 + 3x + 12 you would put "5, 4, 3, 0, 12" in the box to hold the place for the missing ^2.

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. My performance is terrible, I'm not sure how to rate my experience? The class is comfortable, and I like how you teach and I don't feel out of place or weird? I don't know. I have no work ethic, because when I don't understand something I kind of give up on it, I don't have the best attitude towards algebra (5 years of it kind of kills you.) and I have absolutely no motivation (A problem I've struggled with forever.) My goal is to stay at an 82 (which I won't) so I can graduate. I need a miracle. My goal for a final grade is above 80 because I need that to graduate.

6.5 Talk about the Rational Zero Theorem and how you can use it to make a list of the possible rational zeros for a function. How can you use this to find the actual rational zeros?

When you use synthetic substitution to evaluate a polynomial and find it's factors you first take the P (Which is the number without an X, etc) and list all the numbers that go into it. So, for example, if the P is 8, you'd write down +/- {1,8,2 and 4}. Then you do the same for the Q (which is the LC.). When you get all of the numbers, you put the Ps over the Qs to get your possible factors. So, if like in the example above my P was 8 and my Q was, say 1, my possible factors would be +/- {1/1, 8/1, 2/1, and 4/1}; or +/- {1, 8, 2, and 4}. Remember that you have to write the +/- so you don't forget that either of them could be a factor. Then you use synthetic substitution to see if they make a 0.

((I guess I already did that for question 6.3?))

6.6 I need to print out 6.6 to do it.

6.7
 * What is the domain of both these function and explain why this domain is appropriate according to the context of the situation. The domain for Boys is (24.5, infinity] because you can't be negative years old. Girls is (27, infinity] because of the same reason.
 * What is an appropriate range for each function. Explain why this range is appropriate according to the context of the situation. An appropriate range would be (0, 78) because that's the average life span.
 * Find B(7) and G(9). Write what this means in the context of the situation. It means that at age 7, boys are approximately 47 inches tall; and that age 9, girls are approximately 52.5 inches tall.
 * What year is the average height for boys the greatest? ~71.5
 * What is the highest average height for the girls? It doesn't stop on my graph, so I think I did something wrong. Unless there was a typo in the equation that left in positive, and it was supposed to be negative, in which case the highest average is ~50.75 (Which makes no sense.)
 * 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. The one for boys makes sense, it tops at an age of about 71 and a half, and then declines. I can't predict what the height will be for a male at age 45 because it doesn't go that far.