SOLUTION: Explain the transformations on y = (2x)2

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Explain the transformations on y = (2x)2      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1202227: Explain the transformations on y = (2x)2
Found 3 solutions by greenestamps, math_tutor2020, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


We can guess what the question is; but that's not our task....

Re-post your question, with enough of a description so that we know for sure what the question is.

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

I'm assuming the equation is y = (2x)^2 which is the same as y+=+%282x%29%5E2

The parent function y+=+x%5E2 is an upward facing parabola
%0D%0Agraph%28400%2C400%2C-3%2C3%2C-3%2C3%2C-100%2Cx%5E2%29%0D%0A

Replace x with 2x, and the x axis number line will expand by a factor of 2.
I.e. the old input doubles to the new input
x = 4 doubles to x = 8 for instance

The x axis values doubling like this means the x axis number line is stretched out horizontally.
In turn, it gives the illusion the curve is squished horizontally.

Here's a comparison.
The parent function y = x^2 is in green.
The equation y = (2x)^2 is in blue.
%0D%0Agraph%28400%2C400%2C-3%2C3%2C-3%2C3%2C-100%2Cx%5E2%2C%282x%29%5E2%29%0D%0A
The blue graph is horizontally compressed by a factor of 2.

Desmos and GeoGebra are two graphing apps I recommend.

Another way to look at it:
y = (2x)^2 = 4x^2
The jump from y = x^2 to y = 4x^2 is "times 4".
Each old output of the parent function has been quadrupled, which will make the parabola 4 times taller.
A point like (1,1) on the green parent function moves to (1,4) on the blue transformed parabola.
A horizontal squish will be paired with a vertical stretch. Imagine the parabola is a bit of clay that can be molded.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

They want you compare the plot y = (2x)^2 with the plot of the parent function y= x^2.


        There are  TWO  EQUIVALENT  descriptions of this transformation.


One description says that the plot is  COMPRESSED horizontally  with the coefficient of  2.

The other description says that the plot is  STRETCHED  vertically with coefficient of  4.

For given problem,  both these descriptions are  EQUIVALENT,  as I just said above.

They are equivalent, because the function has two equivalent presentations

            y = (2x)^2 = 4*x^2.