Transformations: Vertical compression by a factor of 15 Graph:
We want to describe how to transform the parent function f(x)=x^2 to the graph of the given quadratic function.
h(x)=1/5x^2
To do so, we need to consider four possible transformations.
Vertical translationsNotice that we only need to consider the second transformation.
Stretch or Compression
We have a vertical stretch when x^2 is multiplied by a number whose absolute value is greater than one. If x^2 is multiplied by a number whose absolute value is less than one, a vertical compression will take place.
If x^2 is being multiplied by a negative number, the above still applies but everything will be upside down. In the given exercise, x^2 is multiplied by 15. Therefore, the parent function graph will be vertically compressed by a factor of 15.
Final Graph
Let's now graph the given function and the parent function f(x)=x^2 on the same coordinate grid.
Finally, let's summarize how to draw the graph of the given function when starting with the parent function, f(x)=x^2.
