Exercise 22 Page 52

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

1. Horizontal stretches and shrinks
2. Reflections

   Let's consider them one at the time.

   Horizontal Stretch or Shrink

   We have a horizontal stretch when x is multiplied by a number greater than one. If x is multiplied by a number whose absolute value is less than one, a horizontal shrink will take place.
   
   In the given exercise, x is multiplied by 2. Therefore, the previous graph will be horizontally shrunk by a factor of 12.
   

   Reflection

   Whenever x^2 is multiplied by a negative number, we will have a reflection of the graph across the x-axis.

   

   Note how each x-coordinate stays the same, and how each y-coordinate changes its sign.

   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 horizontal shrink by a factor of 12
   • Reflection in the x-axis