3.3 POLYNOMIAL FUNCTIONS AND MODELS
This lesson has THREE BIG OBJECTIVES :)
A. Identify polynomial functions and their degrees (See ex. 1 page 201
B. Identify the zeros of a polynomial function and their multiplicity. Know how to obtain the degree of a function by adding the multiplicities of the function.
Know when the graph crosses the x-axis and when the graph touches(is tangent to) the x-axis. See pages 204-205
C. analyze the graph of a polynomial function. Know the 4 "End Behavior" rules See pages 206 - 208. Work examples 5 and 6.
I will be online tonight(Sept. 8) from 7 to 9 pm. Leave me a question, comment, or tell me something GOOD that you have learned in lesson 3.3!
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14 comments:
Hey Mrs. Snipes whats up. i was wondering how to do #49 on 3.1 i know its like the number 50 you worked and i wrote it down its just hard for me to start it.
Hey mrs. snipes it devin again. i was lookin through my 3.2 homework and i don't have a question as of now and i am trying to learn all the parent functions.
On lesson 3.3 #19 i put it in the TI- 84 and i could see visually where the graph touched and crossed the x axis but when i tried to use the even and odd r multiplicity theorems to find where they crossed or touched i couldn't figure out what they meant by sign changes
Hi devbrile :)
Not much...just unwinding after a very long day. a)Let's look at what happens when a = 1 and when a = 2.
For a = 1, we get the equation
y = 1(x+3)(x-1) i.e.
y = 1(x^2 + 2x -3)
For a = 2, we get the equation
y = 2(x+3)(x-1) i.e.
y = 2(x^2 + 2x - 3)
b. The value of a does not affect the x-intercepts. If you factor the expression in parenthes, you get the x-intercepts which are still -3 and 1.
c. The axis of sym. does not change. Recall the axis of symmetry is the equation:
x = -b/2a.
For the first equation, Let -b = -2 and a = 1. For the 2nd equation, using the expression in parenthesis, -b still equals -2 and a still equals 1. The 2 outside the paren. is factored out and does not change the value of-b/2a
d. The x coord. of the vertex is
-b/2a, which does not change.
e. The y-coord. of the vertex does change.
It might help you to graph all of these on your graph. calc. and compare the x-int., the axis, and the vertex
If you have more questions, feel free to ask them before 9 :)
You're "overanalyzing" the problem. Here's the scoop on
3.3 # 19: y = 3(x-7)(X+3)^2
7 is a zero of multiplicity 1
-3 is a zero of multiplicity 2.
The graph crosses the x-axis at 7, and is tangent to (touches) the x-axis at -3.
The sum of the multiplicities is 3, so this is a 3rd degree function. For large values of abs. x, the graph will resemble the 3 times the parent function
y = 3x^3.
Devin, I neglected to talk about the "sign change rules" on page 205. Here's what they mean:
If the exponent in an even number, the graph touches the x axis. This means the graph is tangent to the x-axis and does not cross it. If the graph does not cross the x-axis, the sign of y does not change.
if the exponent is an odd number, the graph crosses the x-axis. As the graph crosses the x-axis, the y values change from either positive to negative, or negative to positive. The two boxes on page 205 refer to the y value as
f(x) which is y.
Hi Mrs. Snipes. I wasn't at school today, due to a sore throat and fever, but I should be back tomorrow. Brooke gave be the assignment, and I seemed to be understanding it. But, I still had a question about 65 on 3.1.
Luisa
ps: i don't have my name for this, so i just used my aol
sorry, 66
3.1 prob. 66
This one's for you ozzylu :)
In problem 66, we are given a quadratic equation. p is the independent variable(Think of p as your x) and R is the dependent variable (Think of R as your y).
Now, think about how you find the maximum value for a quadratic equation. .........
The max value is the vertex. The x value of the vertex is -b/2a. The y value of the vertex is found by subbing the value of -b/2a into this quad. equation for p and solving for R. (remember p is your x and R is your y)
So...p = (-1900)/2(-.5)
p = 1900.
R = -.5(1900)^2 =(1900)(1900)
I don't have a calculator handy so you can take it from here. Let me know if you have any more questions.
I'm understanding most of the lesson but I don't understand problem 29. I know we didn't have to work it, but I wanted to make sure that I understanded everything in the lesson. I also am not completely sure how to graph y=x^4, like in problem 43 and 45.
I pretty much understand everything in the first 3 lessons. i can do most of the examples and i didn't have much trouble on the homework so I think I'm doing ok so far.
Mrs. S you will be so proud! I had no problems or questions on this lesson!!! yay for me! I have mastered your BIG 3 OBJECTIVES and think that if we have a quiz it should be on just this lesson...not any of the others :)
Lauren and Emily, I am very glad you had no problems with 3.3. But what about 3.1 and 3.2? See you tomorrow..
I think for the most part, I understand everything. There's just a couple of things I need to go back and look at again. But I'm sure that after being in class tomorrow and you going over everything, I should be just fine:)
Mrs. Snipes! I just had one of those lovely lightbulb moments! I am now understanding some things that were still a little muddled for me today :) However, I am still having a few difficulties with a couple of problems, but I will be by in the morning to get some help with those! Thanks :)
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