Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and /or reflecting. Graph one transformation in each coordinate system. Label each graph. f(x)=-2(x+1)^2+4

- anonymous

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- anonymous

@jim_thompson5910

- jim_thompson5910

I would use something like desmos
https://www.desmos.com/calculator
to graph

- jim_thompson5910

type into the first line
y = x^2
this is the parent function

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## More answers

- anonymous

Okay!

- jim_thompson5910

then you'll shift the graph 1 unit to the left to get y = (x+1)^2
after that, you will multiply the (x+1)^2 term with -2 to get y = -2(x+1)^2. This will reflect the graph over the x axis and vertically stretch the graph by a factor of 2

- anonymous

I have that already on one coordinate plane.

- anonymous

Would shifting be in another coordinate plane?

- jim_thompson5910

finally, you will add 4 to get y = -2(x+1)^2+4
this shifts the graph 4 units up

- jim_thompson5910

each time you do a transformation, you will have it on its own xy axis

- anonymous

I do not understand how do I show this on the (x,y)

- jim_thompson5910

this is what it looks like if you did all equations I mentioned above on the same xy axis

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- jim_thompson5910

imagine each of those parabolas gets its own xy coordinate system

- anonymous

I understand but my teacher wants us to show the change meaning when we plug in -1, 0 and 1

- anonymous

I did get what you got, on each coordinate plane but I have to be able to show the process.

- jim_thompson5910

so he wants you to plug those x values into each equation?

- anonymous

basically

- jim_thompson5910

you can create a table using desmos
click on the equation you want to work with
then click the gear icon
I suggest duplicating the graph, so do so, but it's not mandatory
then turn that duplicate graph into a table

- jim_thompson5910

##### 1 Attachment

- jim_thompson5910

you can add or subtract x values from the table
or change the x values that are already there
the table will update itself with each change or addition in x

- anonymous

Thank you! Now i got it! Are you able to help me with three more questions?

- jim_thompson5910

it depends how long they are, but we'll see

- anonymous

Okay, Suppose the point (2,4) is on the graph of y=f(x). Find a point on the graph of the given function . The reflection of the graph of y=f(x) across the y-axis

- jim_thompson5910

Rule: reflecting any point (x,y) over the y axis will result in (-x,y)

- anonymous

What does the question ask?

- jim_thompson5910

it just wants you to reflect (2,4) over the y axis

- anonymous

How would I do this?

- anonymous

By graphing?

- jim_thompson5910

by using that rule I posted

- anonymous

So instead of 2,4 it would be -2,4

- jim_thompson5910

(-2,4)
don't forget the parenthesis

- anonymous

Yes, and Would I graph this?

- jim_thompson5910

you can if you want
they just want you to find the point

- anonymous

Okay , next question Solve the problem, If f(x)= x-3A/3x+5 and f(3)=6. what is the value of A?

- anonymous

are you able to help me?

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