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

Jun 26, 2017

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), $y = \frac{4}{3} {x}^{2}$ (in blue) and $y = \frac{1}{3} {x}^{2}$ (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 $6$.