Answer:
g(x) = x² - 5
Explanation:
The vertex form of a parabola is:
→ y = (x - a)² + b
where (a, b) is the vertex of the parabola.
From the graph, we can identify that the vertex has been shifted down 5 units, and it has not been shifted horizontally. Therefore, we can assign the following a and b values:
Now, we can plug these into the vertex form equation to get the equation of the function g(x):
y = (x - 0)² + (-5)
This simplifies to:
y = x² - 5