We have a guide graph:
[tex]f(x)=x^2[/tex]
but this function undergoes a series of transformations after altering the function to be expressed as follows
[tex]g(x)=3(x-1)^2+2[/tex]
For this, we must remember the function transformation rules.
1.
[tex]y=g(x-c)[/tex]
Where "c" units are moved horizontally to the right.
That is to say that in our function g(x) the function describes a translation of one unit to the right.
2.
[tex]y=g(x)+c[/tex]
Where "c" units are moved vertically upwards.
That is to say that in our function g(x) the function describes a translation of two units to upwards
3.
[tex]y=c\cdot g(x)[/tex]
Where if c>1 it vertically stretches the graph of y=g(x) by a factor of "c".
That is to say that our function has a vertical stretch by a factor of 3.
In conclusion, the option that meets a vertical stretch with a factor of 3 and a translation of 1 unit to the right and 2 units upward is option C.
