Question

How is the graph of `g(x)=6+4/3x^2` related to the graph of `f(x)=x^2`?

Answer 1

By comparing graphs, we observe that multiplying the square term by an number greater than `1` makes the parabola rise more sharply and adding a constant shifts it vertically.

Explanation:

Please observe the graphs `y = x^2` (in red), `y = 4/3x^2` (in blue) and `y = 1/3x^2` (in green)

For the equation `y = ax^2; a > 0`

The larger that you make the coefficient `a`, the greater the value of `y` for a given value of `x`; this makes the graph rise more sharply.

Please observe the graphs `y = x^2` (in blue) and `y = x^2+6` (in red) the latter is shifted vertically by `6`.