# How are the graphs f(x)=x^2 and g(x)=4(x-3)^2 related?

Jun 20, 2018

$g \left(x\right)$ is shifted 3 units right and stretched vertically by a factor of 4 ($4 \cdot y$). That means $\left(1 , 1\right)$ becomes $\left(1 , 4\right)$ etc. as the graph shows.

#### Explanation:

$f \left(x\right) = {x}^{2}$

graph{x^2 [-10, 10, -5, 5]}

$g \left(x\right) = 4 {\left(x - 3\right)}^{2}$

graph{4(x-3)^2 [-10, 10, -5, 5]}