Transformations: Reflection across the x-axis, vertical compression by a factor of 58 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)=-5/8x^2
To do so, we need to consider four possible transformations.
Vertical translationsNotice that we only need to consider the first and the second transformation.
Reflection
Whenever x^2 is multiplied by a negative number, we will start by reflecting the graph across the x-axis.
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 - 58. Therefore, the previous graph will be vertically compressed by a factor of 58.
Final Graph
Let's now graph the given function and the parent function y=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.
