Question

can someone help me with Polynomial Functions I

Answer 1

Is this a test or a practice assignment?

Answer 2

assignment

Answer 3

my grade is low and i need to get a good grade so any help would be great

Answer 4

What do you understand/recognize, and what do you definitely need help with? I want t to help you learn this material because you'll need it later on, definitely.

Answer 5

well i need to definitely learn how to solve an polynomial equation

Answer 6

Actually for these particular 2 problems you don't need to be able to solve polynomial equations. Rather than me try to teach you that when you don't need it for these questions, I'll suggest you watch this video series sometime later to learn that https://www.khanacademy.org/math/algebra/introduction-to-polynomial-expressions

What parts of these specific questions do you recognize? Do you know what "degree", "term", "coefficient", "end behavior", and so on mean? any words you don't know, or do you know them all but not know how to apply them in the question?

Answer 7

I know what those mean but I dont know how to apply them in questions

Answer 8

Do you know what is degree of polynomial?

Answer 9

Yes isnt that the highest degree or something like that?

Answer 10

Yes ,the highest power of variable

Answer 11

Can you tell me in which parts you need help?

Answer 12

Okay. Let's focus on the 1st question.
1a) What does degree mean? What's the degree of the polynomial equation given? If it's equal to 4, check the box.
1b) What are terms? How many terms does the function have?
1c) What are turning points? What makes a function have turning points? What is the max number of turning points that this function could possibly have?
1d) What is the leading coefficient of the polynomial?
1e) What is the test for if a function is odd? Apply that test
1f) what is 'end behavior'? What would be the end behavior of a polynomail of this degree?
1g) what is a quadratic function? is this polynomial a quadratic function?
1h) when you plug in x=1, is y = f(1) = -3?
1i) When you plug in x=0, is the y-intercept of the graph at (0,3), is y = 3?

Answer 13

i dont know how to check for any of that

Answer 14

i believe the last 2 are right

Answer 15

1a) What does degree mean? What's the degree of the polynomial equation given? If it's equal to 4, check the box.
Let's break it down. You know what degree means. What is the degree of the polynomial equation given? You can do it!

Answer 16

itd be 4 no?

Answer 17

That's correct! So the first box is checked. Next:
1b) What are terms? How many terms does the function have?
1c) What are turning points? What makes a function have turning points? What is the max number of turning points that this function could possibly have?

Answer 18

1b) 3 terms i think
1c) it only has 2

Answer 19

I dont think y can be a term

Answer 20

1b you have the correct answer! Nice :) you're correct that y isn't a term.
For 1c, "Any polynomial of degree n can have a minimum of zero turning points and a maximum of n-1" (not my words, Google-crafted). You know the polynomial is degree 4, so what is the max number of turning points? 4=n, and max is n-1

1d) What is the leading coefficient of the polynomial?
1e) What is the test for if a function is odd? Apply that test

Answer 21

so theres no turning points?

Answer 22

No, there are turning points. The polynomial we're looking at has degree n=4, and the max number of turning points is n-1. What is the max number, then?

Answer 23

oh so would you have to do 4-1 to get 3 turning points?

Answer 24

That's correct! Good work. (so far, we have this:
1a ) true
1b) false
1c) true )

Let's keep going!
1d) What is the leading coefficient of the polynomial?
1e) What is the test for if a function is odd? Apply that test

Answer 25

A coefficient is a number and a variable so 1 couldn't be ?

Answer 26

The coefficient is just the number part. in 3x^10, 3 is the coefficient, and 3x^10 is the entire term. So what is the leading, the first coefficient in the polynomial?

Answer 27

Oh so 7 is the coefficient

Answer 28

Well, in our case which term is the /first/ term of the polynomial?
(7 is the coefficient of the 2nd term, but what is the coefficient of the /leading/ term)?

Answer 29

It would be 1 because theres an invisible 1 before x^4

Answer 30

Yep! ( so far, we have this:
1a ) true
1b) false
1c) true
1d) true)

1e) What is the test for if a function is odd? Apply that test
1f) what is 'end behavior'? What would be the end behavior of a polynomail of this degree?

Answer 31

1f ) i wanna say it going up and up and the other one im not to sure on odd functions

Answer 32

I say its up because of this http://www.wolframalpha.com/input/?i=y%3Dx%5E4-7x%5E2%2B13&lk=4

Answer 33

You are correct on 1f). Can you explain/understand it without using wolframalpha? you don't need to rely on tools like that, I know you can figure it out! As the value of x increases to the right, what happens to y? As the value of x decreases to the left, what happens to y?

For 1e) the test for if a function is odd is substituting -x for all x's in the equation, and seeing if this is equal to -f(x). So if -f(x) = f(-x), the function is odd. Reminder that when you replay you have to take the whole value of -x to powers, not just the x part.

1g) what is a quadratic function? is this polynomial a quadratic function?

Answer 34

Well if X increases i would assume that happens to the other side Y

so theres 2 odd functions ?
Quadratic function is where the numbers dont equal to zero, how would i know if it equals to zero?

Answer 35

for 1e) you're doing two different things to the same function, and then seeing if they are equal. The first thing is substituting in -x in place of every x. The second thing is finding
-f(x), so multiplying the original function by -1. You check if these two things are equal, and if they are this is an odd function.

For 1g) Quadratic function are second-degree polynomials.

Let me know if you've got this.

Answer 36

so you write it out as -x^4 + 7x^2 + y - 13

Answer 37

To apply the test for odd functions, I would first take the function f(x) and put a -x for every x.
So f(x) = x ^4 - 7 x ^2 + 3.
f(-x) = (-x) ^4 - 7 (-x) ^2 + 3.
What does this simplify to, for 1e?
When you mutiply the entire function by -1 to get -f(x), what do you get? -y = ?

Answer 38

0?

Answer 39

0 isn't the answer to either of those questions.
1e, part 1) f(-x) = (-x) ^4 - 7 (-x) ^2 + 3 simplies to what?

1e, part 2) When you mutiply the entire function by -1 to get -f(x), what do you get? -y = ?

Answer 40

Hmm i dont know

Answer 41

You can do it! Simplify f(-x) = (-x) ^4 - 7 (-x) ^2 + 3 piece by piece. The first term, (-x) ^4, is equal to x^4 because -x * -x = x^ 2 and doing this twice is x^4. Keep going from there!

And you can definitely multiply the whole function by -1. I believe you can do it.
-f(x) = -y = -1 * (x ^4 - 7 x ^2 + 3) and simplify.

Answer 42

x^4 +3 = f(-x)+7x^2

Answer 43

Are you trying to combine the two parts for the test for odd functions? first let's completely work out what each one is, on its own.

for part 1, (-x)^4 simplifies to x^4. What does 7(-x)^2 simplify to? All of this is f(-x).

for part 2, what is -f(x), where you have -f(x) = -y = -1 * (x ^4 - 7 x ^2 + 3)? simplify.

Answer 44

7x^2

Answer 45

Do i put that where the (x) is ?

Answer 46

the (x) in f(x) means that y is equivalent to f, the function, with the input of a value x.

So for part 1, we have x^4 - 7 x^2 + 3
for part 2, what do we have?

Answer 47

-f(x) = -y = -1 isnt that what we use

Answer 48

No, you have to multiply the entire equation by -1 for part 2.
-f(x) = -y = -1*(x ^4 - 7 x ^2 + 3) and simplify the left side.

Answer 49

i dont know the -1 one cancels the other -1 right?

Answer 50

There's no canceling here, you need to find the equation for -f(x). This is the second part of the test for odd functions. -f(x) = -y = -1*(x ^4 - 7 x ^2 + 3)
Do /not/ take -1 from the whole thing, the point is to find -f(x). You have to compare this to what we got for the first part.

Answer 51

okay now im lost

Answer 52

how are you supposed to compare

Answer 53

The 2nd part of this test is finding the value of -f(x). You can't cancel out the -1 because you first need to find -f(x), where you mulitply the original polynomial equation.

You need to simplify the 2nd part of the test for odd functions, and /then/ you can compare them. You compare them by seeing if the two parts are equal or not.

Answer 54

they dont look equal to me

Answer 55

That is correct. What is the 2nd part found, then? Show me that you know what -f(x) is.
f(-x) was the first part, which was f(-x) = x^4 - 7 x^2 + 3

1g) what is a quadratic function? is this polynomial a quadratic function?
1h) when you plug in x=1, is y = f(1) = -3?

Answer 56

I dont know what f(x) is .. its just like common sense theres no way f(x) -y = -1 could ever equal to x^4-7x^2+3

Answer 57

its just something you can tell

Answer 58

No, that's not what the test is. f (x) is EQUAL to y, so -f(x) is EQUAL to -y. This is /not/ equal to -1, I think you misread something. For the second part of this test, you are supposed to take the polynomial, f(x) = y = x ^4 - 7 x ^2 + 3 in this case, and /multiply/ the entire thing by -1. There is no = -1 in this.

Answer 59

oh okay

Answer 60

Let's move on to the last 3 parts of the 1st question.
1g) what is a quadratic function? is this polynomial a quadratic function? (earlier I told you that a quadratic is a 2nd degree polynomial)
1h) when you plug in x=1, is y = f(1) = -3?
1i) When you plug in x=0, is the y-intercept of the graph at (0,3), is y = 3?

Answer 61

wait i still dont know if its quadratic or not

Answer 62

wait it is because its goes up and up right?

Answer 63

for 1g, what degree is this polynomial? A quadratic polynomail is a 2nd degree polynomial. Is this one? (no, not because it goes 'up and up right')
h) when you plug in x=1, is y = f(1) = -3?
1i) When you plug in x=0, is the y-intercept of the graph at (0,3), is y = 3?

Answer 64

yes?

Answer 65

the last 2 are right

Answer 66

You are correct for 1h and 1i. What about 1g?

Answer 67

G i dont know all i know is that its 2nd degree polynomial

Answer 68

but that doesnt help with the answer

Answer 69

Well a quadratic function has degree 2. What degree is this function? Is this function quadratic?

Answer 70

oh so then yeah it would be quadratic because its 2nd poly. sorry i got lost i had to re read it

Answer 71

right?

Answer 72

No, it is not quadratic. It does have a 2nd degree term, but it is NOT a 2nd degree function. We found in 1a that it is a 4th degree function. So the answer to 1g is?

Answer 73

is not a quadratic function

Answer 74

That's correct. Do you understand the parts of question 1 well, now? If you do we can move on to question 2.

Answer 75

Yes we cant move onto 2

Answer 76

can**

Answer 77

This graph has nothing to do with the equation on top right?

Answer 78

Okay. (they are not related, yes)
2a) You know the equation turn points = n -1, where n is the degree of the function. How can you use this to find the least possible degree by looking at the graph of the function?
2b) Remember what the leading coefficient is? How can you tell what the sign of it is from the graph?
2c) Hint, you use this in 2a. It's easily countable by looking at the graph.
2d) What is the y-intercept of a graph? What's the y-intercept of this graph?
2e) what happens at the left and right ends of this graph?

Answer 79

A) where it hits zero ?

Answer 80

That's actually the answer to a different part of this question, but it's not the answer to 2a.

2a) You know the equation turn points = n -1, where n is the degree of the function. How can you use this to find the least possible degree by looking at the graph of the function?

2b) Remember what the leading coefficient is? How can you tell what the sign of it is from the graph?

Answer 81

The coefficient is 0?

Answer 82

2a) You know the equation turn points = n -1, where n is the degree of the function.
TURNING POINTS = DEGREE OF THE FUNCTION - 1
How can you use this to find the least possible degree by looking at the graph of the function?

for 2b), no, like you said before, there's an invisible number in front of the leading term. That number (not the variable part) is the leading coefficient.

Answer 83

Oh that's right so 1 is the coefficient

Answer 84

You've got 2b right! What about 2a?
2a) You know the equation turn points = n -1, where n is the degree of the function.
TURNING POINTS = DEGREE OF THE FUNCTION - 1
How can you use this to find the least possible degree by looking at the graph of the function?

Answer 85

I dont know is there a formula that you have to use?

Answer 86

I've given you the formula that you need for 2a.
MAX TURNING POINTS = DEGREE OF THE FUNCTION - 1
You need to solve for the least possible degree of the function.

Answer 87

I dont know what number to put in for 1- (-1)

Answer 88

Are you trying to say that you found 1 turning point, and subtracting -1 from both sides? (by the way, when you subtract a negative number, you add the abs value. $3 of debt would be -3. if someone cleared you of $1 of that debt, or subtracted -1, you'd be $2 in debt, -2.

There are more than 2 turning points in this graph. Count again.

MAX TURNING POINTS = DEGREE OF THE FUNCTION - 1
You need to solve for the least possible degree of the function.

Answer 89

Looks like theres 4

Answer 90

"A Turning Point is an x-value where a local maximum or local minimum happens". Count again.

Answer 91

3?

Answer 92

Are you sure? How many local minimums or maximums can you see?

Answer 93

2 min and 1 max

Answer 94

2a) I can only see one local minimum. For it to be a minimum, you must be able to tell that it is /definitely/ a minimum, and the line leading down to the bottom right doesn't count. So with # of turning points = 2, use this equation

MAX TURNING POINTS = DEGREE OF THE FUNCTION - 1
You need to solve for the least possible degree of the function.

Answer 95

3?

Answer 96

that's correct! (sorry, my browser had some issues)
2b) Remember what the leading coefficient is? How can you tell what the sign of it is from the graph?
2c) Hint, you use this in 2a. It's easily countable by looking at the graph.