Exercise 5 Page 50

We want to describe how to transform the parent function f(x)=x^2 to the graph of the given quadratic function. y=3(x-1)^2 To do so, we need to consider two possible transformations.

1. Vertical stretches and shrinks
2. Horizontal 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 3. Therefore, the graph of f will be vertically stretched by a factor of 3.
   

   Horizontal Translation

   If an addition or subtraction is applied to only the x-variable, the graph will be horizontally translated. In case of addition, the graph will be translated to the left. In case of subtraction, it moves to the right. In the given equation, 1 is being subtracted from x, so the graph will be translated one unit to the right.

   

   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 stretch by a factor of 3
   • A horizontal translation 1 unit right