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

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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

Mathematics
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I would use something like desmos https://www.desmos.com/calculator to graph
type into the first line y = x^2 this is the parent function

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Okay!
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
I have that already on one coordinate plane.
Would shifting be in another coordinate plane?
finally, you will add 4 to get y = -2(x+1)^2+4 this shifts the graph 4 units up
each time you do a transformation, you will have it on its own xy axis
I do not understand how do I show this on the (x,y)
this is what it looks like if you did all equations I mentioned above on the same xy axis
imagine each of those parabolas gets its own xy coordinate system
I understand but my teacher wants us to show the change meaning when we plug in -1, 0 and 1
I did get what you got, on each coordinate plane but I have to be able to show the process.
so he wants you to plug those x values into each equation?
basically
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
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
Thank you! Now i got it! Are you able to help me with three more questions?
it depends how long they are, but we'll see
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
Rule: reflecting any point (x,y) over the y axis will result in (-x,y)
What does the question ask?
it just wants you to reflect (2,4) over the y axis
How would I do this?
By graphing?
by using that rule I posted
So instead of 2,4 it would be -2,4
(-2,4) don't forget the parenthesis
Yes, and Would I graph this?
you can if you want they just want you to find the point
Okay , next question Solve the problem, If f(x)= x-3A/3x+5 and f(3)=6. what is the value of A?
are you able to help me?

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