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

Question

1180 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-04T16:14:05

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

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 $g(x)$ .

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