We have been given that that function [tex]y=3(x-5)^2[/tex] is obtained from the graph of [tex]y=x^2[/tex]. We are asked to find the two transformations that can be used to obtain the transformed function.
We will use transformation rules to solve our given problem.
[tex]f(x-a)\Rightarrow\text{Graph shifted to the right by a units}[/tex], where a is any positive number.
We can see that the value of a is 5 for our given function, therefore, graph is shifted to right by 5 units.
Now we will use scaling rules.
[tex]f(x)\Rightarrow a\cdot f(x)[/tex]
If [tex]a>1[/tex], then function is stretched vertically by a factor of 'a'.
If [tex]a<1[/tex], then function is compressed vertically by a factor of 'a'.
We can see that value of a is 3. Since 3 is greater than, so function will be stretched vertically by a factor of 3.
Therefore, the function can be obtained by a vertical stretch and translation of 5 units to right and option J is the correct choice.
