Question

I'm in desperate need of help
Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages.
f(x) = 3(x - 2)^2 + 1

Answer 1

The original function is the parabola with vertex on (0,0)

f(x) = x^2

Answer 2

For

f(x) = a*f(x - b) + c

the a,b,and c values change the function.

b - shift in horizontal direction
c - shift in vertical direction
a - squeeze or stretch the graph vertically

Answer 3

\[f(x) = 3*(x-2)^2 + 1\]

horizontal shift by 2, moves the +x direction 2
vertical shift by 1, moves the +y direction 1
stretches the graph vertically by a factor of 3

Answer 4

Let me start by saying thank you so much for that I appreciate it but I'm still confused of how I would write that like when you're talking about the +x direction 2 and +y direction 1 could you show me please just like a rough example of it?

Answer 5

hint:
read all about it here:
https://www.mathsisfun.com/sets/function-transformations.html

Answer 6

To address your specific question:

Suppose you start with the graph of y=x^2.

Were you to translate (move or shift) this graph "a" units to the right, the function would become y=(x-a)^2.

"a" units to the left, the function would become y=(x+a)^2.