Exercise 23 Page 52

We want to describe how to transform the parent function y=x^2 to the graph of the given quadratic function. y=1/5x^2-4 To do so, we need to consider two possible transformations.

1. Vertical stretches and shrinks
2. Vertical translations

   Let's consider them one at the time.

   Vertical Stretch or Shrink

   We have a vertical stretch when x^2 is multiplied by a number greater than one. If x^2 is multiplied by a number less than one, a vertical shrink will take place.
   
   In the given exercise, x^2 is multiplied by 15. Therefore, the graph of f will be vertically shrunk by a factor of 15.
   

   Vertical Translation

   If an addition or subtraction is applied to the whole function, the graph will be vertically translated. In the case of addition, the graph will be translated up. In the case of subtraction, it will be moved downwards. In the given equation, 4 is subtracted from the whole function, so the previous graph will be translated 4 units down.

   

   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 all the transformations of the graph of f.

   • A vertical shrink by a factor of 15
   • A vertical translation 4 units down