Question

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

Answer 1

@jim_thompson5910

Answer 2

I would use something like desmos

https://www.desmos.com/calculator

to graph

Answer 3

type into the first line

y = x^2

this is the parent function

Answer 4

Okay!

Answer 5

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

Answer 6

I have that already on one coordinate plane.

Answer 7

Would shifting be in another coordinate plane?

Answer 8

finally, you will add 4 to get y = -2(x+1)^2+4

this shifts the graph 4 units up

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

imagine each of those parabolas gets its own xy coordinate system

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

basically

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

What does the question ask?

Answer 24

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

Answer 25

How would I do this?

Answer 26

By graphing?

Answer 27

by using that rule I posted

Answer 28

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

Answer 29

(-2,4)

don't forget the parenthesis

Answer 30

Yes, and Would I graph this?

Answer 31

you can if you want

they just want you to find the point

Answer 32

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

Answer 33

are you able to help me?