Polynomial Graphing Question (1 Viewer)

[starryblue]

Would anyone tell me how to graph this question:
y=2x(x-1)(x+2)

tys for the help =)

 

[_deloso]

Would anyone tell me how to graph this question:
y=2x(x-1)(x+2)

tys for the help =)

for x intercept let y=0
therefore x int=0, 1 and -2

for y intercept, let x=0 therefore y=0

now plot those intercepts and then sub in x=3 to test whether it is positive or negative, if it is positive then start above the x axis, if it is negative then start below the x axis

it's really hard to explain without actually drawing out but your graph should look something like this. ∩U well sorta like that but connected.. you know like a wave graph

 

[starryblue]

for x intercept let y=0
therefore x int=0, 1 and -2

for y intercept, let x=0 therefore y=0

now plot those intercepts and then sub in x=3 to test whether it is positive or negative, if it is positive then start above the x axis, if it is negative then start below the x axis

it's really hard to explain without actually drawing out but your graph should look something like this. ∩U well sorta like that but connected.. you know like a wave graph

umm...why sub in x=3? as in why 3?

 

[funnytomato]

the actual graph would look like http://www.wolframalpha.com/input/?i=plot+y=2x(x-1)(x+2)
but the scales are kinda confusing, imagine it being streched out vertically

so once you get the intercepts, you need to know the general shape of a cubic function(deduce it from the intercepts/sign of y at each interval between the intercepts, behavior for large +ve/-ve x values)

you have to draw a curve passing through all the 3 x intercepts and goes to +ve infinity as x approaches +ve infinity and
goes to -ve infinity as x approaches -ve infinity (or sub in large numbers using a calculator)

then you can find f'(x) and find its stationary points

 

[funnytomato]

umm...why sub in x=3? as in why 3?

it doesn't have to be 3, that's just an example

so you have to test values in:
x<-2
-2<x<0
0<x<1
x>1
to find out the sign of y(i.e. is it above or below the x axis)

 

[_deloso]

umm...why sub in x=3? as in why 3?

cos to determine where the graph is at when it is greater than 1 cos 1 is an x intercept. I mean you dont have to sub in 3, you can also sub in 2 or 5 as long as it is greater than 1. so when you are drawing the graph, you will know if it goes from positive to negative or negative to positive where 1 is the "changing point". and when i say positive and negative, im talking in relation to the y value.

 

[MrBrightside]

or you could use stationary points by finding derivatives and max min turning points.

 

[starryblue]

it doesn't have to be 3, that's just an example

so you have to test values in:
x<-2
-2<x<0
0<x<1
x>1
to find out the sign of y(i.e. is it above or below the x axis)

thank you. can you teach me how to do another graphing question?

x^2/4 + 4y^2 = 1

how would you graph that then?

 

[funnytomato]

thank you. can you teach me how to do another graphing question?

x^2/4 + 4y^2 = 1

how would you graph that then?

from the unit circle x^2 + y^2 =1,
to (x/2)^2 + (y/0.5)^2 = 1 , you're stretching the unit circle horizontally by a factor a 2, and shrinking vertically to half

 

[funnytomato]

so it's an ellipse with x intercepts at x=2 and x=-2, y intercepts 1/2 and -1/2

 

[starryblue]

from the unit circle x^2 + y^2 =1,
to (x/2)^2 + (y/0.5)^2 = 1 , you're stretching the unit circle horizontally by a factor a 2, and shrinking vertically to half

sorry but i don't understand how you got (x/2)^2 + (y/0.5)^2 = 1...

 

[_deloso]

or you could use stationary points by finding derivatives and max min turning points.

lol yeah you could but I think he/she is still in year 11..

 

[SpiralFlex]

lol yeah you could but I think he/she is still in year 11..

Starry is in Year 10. I am pretty sure she has learnt max/min points.

 

[starryblue]

Starry is in Year 10. I am pretty sure she has learnt max/min points.

" i have?

 

[SpiralFlex]

This is in the form of an ellipse,



In this case,






The indicates a stretch of 2 units horizontally.

The indicates a shrinking of a half units vertically.

" i have?

Sorry I assumed your tutoring college has covered it. My mistake.

 

[starryblue]

This is in the form of an ellipse,



In this case,






The indicates a stretch of 2 units horizontally.

The indicates a shrinking of a half units vertically.



Sorry I assumed your tutoring college has covered it. My mistake.

omg...i vaguely remember doing something like that...i shall check my notebk...

 

[SpiralFlex]

omg...i vaguely remember doing something like that...i shall check my notebk...

*Eats notebook*

 

[starryblue]

*Eats notebook*

Nooo~

btw, it's not in my notebk...== what the heck, i swear i've seen something like that before...strange :L

 

[SpiralFlex]

Nooo~

btw, it's not in my notebk...== what the heck, i swear i've seen something like that before...strange :L

You probably seen it in the Cambridge book. Or maybe in a past life as a mathematician.

 

[starryblue]

You probably seen it in the Cambridge book. Or maybe in a past life as a mathematician.

i think i was hallucinating...i'm sad )= happy now?