Polynomial Graphing Question (2 Viewers)

[SpiralFlex]

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

Yes, I most enjoy it when humans are sad.

 

[starryblue]

Yes, I most enjoy it when humans are sad.

hmmph...unfortunately for you, that my sadness lasts for a maximum of 5 mins, i'm back to normal now

 

[starryblue]

how do u sketch x=1/2 y(y-2) and x= 2y(y-2) on the same graph?

 

[SpiralFlex]

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

Continuing from his method. Year 10 method. You will learn Calculus in Year 11 and find a more efficient method. For now this method will do.

Finding intercepts

and intercepts.

I like better than . So we will find the intercept first.

intercept: Let





Now,

Let





Plot this into your graph. Your graph should now look like this.




Now you have a dilemma. Where should you start your graph? There are two possible starting points. Top of the axis or the bottom of the axis. So how do we decide?



If we look at our equation of our graph,



If we expand it out, we get . Since the power of three is the highest power, we will inspect the coefficient of it. It is . Two is a positive number. So we will start from the top.

It will start here!




Now, we will consider three possible drawings.

SMOOTH LINE![ONE DEGREE]





BOUNCE OFF (REJECTION!)[EVEN DEGREE]




HORIZONTAL INFLEXION (JINK/HUMP) [ODD DEGREE]





So let's consider the first intercept it will cross. Our closest one is 1. We can see that,

was our graph.

Let's focus on . It has a degree of 1. So it will be a smooth line forward.




Our next intercept is 0. Let's focus on . It has a degree of 1. So it will also be a smooth line.

So your graph is now like this.




Finally the intercept is -2. Let's focus on . It has a degree of 1. So it will also be a smooth line.

So your graph is like this.

 

[SpiralFlex]

how do u sketch x=1/2 y(y-2) and x= 2y(y-2) on the same graph?

Do you mean?

and ?

 

[funnytomato]

how do u sketch x=1/2 y(y-2) and x= 2y(y-2) on the same graph?

you know how to draw the basic parabola y=k(x-a)(x-b), right?
it's like y= k (x-0) (x-2) , so the constant k would change the magnitude/"height" of the function value y

so on the same graph, the one with a higher constant would be always further away/have a higher magnitude than the one with a lower constant. i.e. curve with larger k is higher than the other one for y>0, lower for y<0

also you need to change the orientation of the graph, so it's like concave "right" instead of concave up

 

[lilly luta]

Continuing from his method. Year 10 method. You will learn Calculus in Year 11 and find a more efficient method. For now this method will do.

Finding intercepts

and intercepts.

I like better than . So we will find the intercept first.

intercept: Let





Now,

Let





Plot this into your graph. Your graph should now look like this.




Now you have a dilemma. Where should you start your graph? There are two possible starting points. Top of the axis or the bottom of the axis. So how do we decide?



If we look at our equation of our graph,



If we expand it out, we get . Since the power of three is the highest power, we will inspect the coefficient of it. It is . Two is a positive number. So we will start from the top.

It will start here!




Now, we will consider three possible drawings.

SMOOTH LINE![ONE DEGREE]





BOUNCE OFF (REJECTION!)[EVEN DEGREE]




HORIZONTAL INFLEXION (JINK/HUMP) [ODD DEGREE]





So let's consider the first intercept it will cross. Our closest one is 1. We can see that,

was our graph.

Let's focus on . It has a degree of 1. So it will be a smooth line forward.




Our next intercept is 0. Let's focus on . It has a degree of 1. So it will also be a smooth line.

So your graph is now like this.




Finally the intercept is -2. Let's focus on . It has a degree of 1. So it will also be a smooth line.

So your graph is like this.

Spiral !!! :O