Question

How are the graphs `f(x)=x^2` and `g(x)=3x^2+6` related?

Answer 1

The graph of `g(x)` can be described as a transformation of the graph of `f(x)`.

Explanation:

First, take a look at the graph of `f(x)`.
graph{x^2 [-30, 30, -10, 10]}

Now look at the graph of `g(x)`.
graph{3x^2 + 6 [-30, 30, -10, 10]}

The graph of `f(x)` is vertically stretched by a factor of 3, and then translated up 6 units to get the graph of `g(x)`.