Question

Its asking a lot but... can someone guide me through a few of these questions and show me what to do?

Answer 1

that's better

Answer 2

Thanks c:

Answer 3

^ ty organic Latte

Answer 4

a polynomial of degree 3 can have at most 3 zeros
it must have one zero
it cannot have more than 3 because if you have say zeros at \(r_1,r_2,r_3\) then the polynomial will factor as
\[p(x)=a(x-r_1)(x-r_2)(x-r_3)\]

Answer 5

Is there a way for them both to be correct? Explain your answer.
No
a zero of a polynomial is a synonym for where it crosses the \(x\) axis
if \(r\) is a zero then \(p(r)=0\) and so \((r,0)\) is on the graph

Answer 6

So since it has a degree of 3 it crosses the x axis 3 times?

Answer 7

i can cross once only
like for example \(y=x^3\) only crosses once at \((0,0)\)
http://www.wolframalpha.com/input/?i=y%3Dx^3

Answer 8

Ohhh i see

Answer 9

i can have two zeros, touch once and cross once
http://www.wolframalpha.com/input/?i=y%3Dx^2%28x-2%29

Answer 10

or it can cross three times
http://www.wolframalpha.com/input/?i=y%3D%28x-2%29%28x%2B1%29%28x-4%29

Answer 11

Thank You c:

Answer 12

yw

Answer 13

for part two i would pick
\[g(x) = x^3 – x^2 – 4x + 4\] because it is easiest

Answer 14

Then i graph and show the zeros right?

Answer 15

a rational zero of this polynomial has to divide 4
it is pretty obvious that \(g(1)=1-1-4+4=0\)

Answer 16

yeah you can graph it and also factor it
here is the graph
http://www.wolframalpha.com/input/?i=y%3D+x^3+%E2%80%93+x^2+%E2%80%93+4x+%2B+4

Answer 17

So it has 3 zeros?

Answer 18

you can see that the graph crosses the x axis at \(-2,1,2\)
yes three zeros

Answer 19

since those are the zeros that means
\[g(-2)=0\\
g(1)=0\\
g(2)=0\] and it also means that it factors as
\[g(x)=(x+2)(x-1)(x-2)\]

Answer 20

And the y intercept is 5 right?

Answer 21

the \(y\) intercept is at \(g(0)=4\) the constant, so no not \(5\)\
\((0,4)\) is on the graph

Answer 22

Oh ok... So The Y intercept is 4 because that is where it intercepts the y axis, There are 3 zeros which are \[-2,1,2 \] But I don't get what it means by if it opens upwards or downwards :/

Answer 23

i am not sure what that means either because it is not a quadratic

Answer 24

Maybe because it shows up in the graph from the bottom?

Answer 25

i would say it does neither and this is a mistake in the question
you can see the graph from the wolfram link i sent

Answer 26

i would say it does not open up or down, but goes from \(-\infty\) to \(+\infty\)
that is more accurate

Answer 27

Oh Ok Thanks c:

Answer 28

yw

Answer 29

you good with this one
4) Esmeralda is graphing a polynomial function as a parabola. Before she begins graphing it, explain how to find the vertex. Make sure you include how to determine if it will be a maximum or minimum point. Use an example quadratic function to help you explain and provide its graph.?

Answer 30

Um... im not really sure... does it come with any equation?

Answer 31

Oh you make an example?

Answer 32

How do you find the x value of the vertex?

the \(x\) values of the vertex of \(y=ax^2+bx+c\) is \(-\frac{b}{2a}\)

Answer 33

you want to make up an example? if so make it easy
like \(y=x^2+4x-2\) in which case the \(x\) coordinate of the vertex would be
\[-\frac{4}{2\times 1}=-2\]

Answer 34

Oh ok... do you simplify it?

Answer 35

How do you find the y value of the vertex?

That is easy enough, plug in the \(x\) values to find the \(y\) value
in our example since the \(x\) coordinate of the vertex is \(-2\) the \(y\) coordinate is
\[y=(-2)^2+4\times (-2)-2=4-8-2=-6\]

Answer 36

lol you do not "simplify" it, you compute it

Answer 37

well the bottom lol 2 times 1

Answer 38

i picked an easy example so that it would be an integer, not a fraction

Answer 39

Oh ok lol now i see XD silly me... but again it shows if it opens upwards or downwards...

Answer 40

now this time that makes sense
a parabola opens up or down
lets graph the example i wrote
http://www.wolframalpha.com/input/?i=y%3Dx^2%2B4x-2

Answer 41

it is real real easy to tell if it opens up or opens down
\[y=ax^2+bx+c\] opens up if \(a>0\) and opens down if \(a<0\)
i.e. it opens up if the leading coefficient is positive and opens down if the leading coefficient is negative

Answer 42

Ohhh ok

Answer 43

How can he tell if the function has an even or odd degree?

if it goes from \(-\infty\) to \(+\infty\) or vice versa, the degree is odd
like \(y=x,y=x^3\) etc

Answer 44

it it goes from \(+\infty \) to \(+\infty\) or \(-\infty\) to \(-\infty\) the degree is even
like \(y=x^2\)

Answer 45

Does this mean that he can determine the exact number of degrees the function has?
hell no

you could have a fifth degree polynomial that has 3 zeros just like a 3rd degree polynomial
or a fourth degree polynomial that looks like a quadratic

Answer 46

lol
Thank You so very much... I really appreeciate it c:

Answer 47

*apreciate

Answer 48

yw
hope it is more or less clear
sorry about that stupid spam at the beginning
i suspended them

Answer 49

Lol Thanks... It was weird :s lol its really rude when people do that though...

Answer 50

lol