Answer:
g(x) = (x - 3)² - 4
Explanation:
When values are directly added to the "x" variable (usually inside of parentheses), the function shifts to the left that many units.
When values are directly subtracted from the "x" variable, the function shifts to the right that many units.
When values are added to an overall function, the function shifts upwards that many units.
When a value is subtracted from an overall function, the function shifts downwards that many units.
We can determine how the function has been translated by looking at the changed position of the vertex (the lowest point of the line).
As you can see, the new vertex now lies on x = 3 rather than x = 0.This means that there should be a -3 directly next to the "x" variable in the new function.
The new vertex also now lies on y = -4 rather than y = 0. Therefore, there should be a -4 added to the overall equation.
These changes make the new function:
g(x) = (x - 3)² - 4