Exercise 2 Page 84

We want to describe how to transform the parent function f(x)=x^2 to the graph of the given quadratic function. g(x)=(x-7)^2+2 To do so, we need to consider two possible transformations.

1. Horizontal translations
2. Vertical translationsLet's consider them one at the time.

   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 will be moved to the right. In the given equation, 7 is being subtracted from x, so the previous graph will be translated 7 units to the right.

   

   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, 2 is added to the whole function, so the previous graph will be translated 2 units up.

   

   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 how to draw the graph of the given function when starting with the parent function, f(x)=x^2.

   • Translation 7 units to the right
   • Translation 2 units up