Question

Help with #8

Answer 1

@jim_thompson5910 Do you know how to do #8?

Answer 2

@surjithayer

Answer 3

I JUST DID THIS IN CLASS

Answer 4

Okay this is easy 1 second

Answer 5

Ok cool! :)

Answer 6

You know how to write it in standard form, yes?

Answer 7

Just write it in descending order of exponents.

Answer 8

Then the degree is 3. This is because it is the highest exponent.

Answer 9

Also, the degree is odd because it is 3. This means it has 3 solutions concluding that the end behavior must be different.

Answer 10

Ok so \[y=x^{3}+2x ^{2}-4x+8\]

Answer 11

That is correct, nice job

Answer 12

Ok, and the end behavior of the graph?

Answer 13

Well the degree is 3 right? This is because it's the highest exponent. The degree tells us how many SOLUTIONS the equation has. This means that the end behavior must be different. Either the graph will rise right, or fall left. We do not know since we are not given the leading coefficient.

Answer 14

So basically, if the degree is odd, the end behavior is always different. For an even degree, the end behavior would be the same.

Answer 15

Ok thanks! Did you already do this assignment?

Answer 16

No, I take algebra 2 at a public school.

Answer 17

Ah, ok. Do you think you could help me with a few more?

Answer 18

Yeah, of course.

Answer 19

Is it the same worksheet you linked?

Answer 20

Yeah, the next one is #14. I'll open a new question!

Answer 21

Ok, cool

Answer 22

\[y=x^3+2x^2-4x+8\]
it is a polynomial of 3rd degree
so three solutions.
\[\frac{ dy }{ dx }=3x^2+4x-4\]
\[\frac{ dy }{ dx }=0,~gives~3x^2+4x-4=0\]
\[3x^2+6x-2x-4=0\]
\[\left( x+2 \right)\left( 3x-2 \right)=0,x=-2,\frac{ 2 }{ 3 }\]
tangent is parallel

Answer 23

tangent is parallel to x-axis at x=-2,2/3

Answer 24

@surjithayer She already got the answer.

Answer 25

\[\frac{ d^2y }{ dx^2 }=6x+4\]
at x=-2
\[\frac{ d^2y }{ dx^2 }=-8<0\]
hence there is maxima at x=-2
similarly it has minima at x=2/3
when x=-2
y=-8+8+8+8=16
whenx=2/3
\[y=\frac{ 8 }{ 27 }+\frac{ 8 }{ 9 }-\frac{ 8 }{ 3 }+8=\frac{ 8+24-72+216 }{ 27 }=\frac{ 176 }{ 27 }=6\frac{ 14 }{ 27 }\]
now we can draw the graph