Exercise 17 Page 582

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

1. Reflections
2. Stretches and compressions
3. Horizontal translations
4. 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.

   

   In the given exercise, x^2 is multiplied by 2. Therefore, the parent graph will be vertically stretched by a factor of 2.

   

   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.

   • Vertical stretch by a scale factor of 2