the graph below has the same shape as the graph g(x)=x^2 but it is shifted down 3 units and to the left 2 units what is this equation

Option (C)

Step-by-step explanation:

Parent function g(x) = x² [Vertex at the origin (0, 0)]

When this function is shifted 3 units down,

Rule to be followed,

g(x) → g(x) - 3

So, g'(x) = x² - 3

Followed by 2 units shift to the left,

Rule to be followed,

g'(x) → g'(x + 2)

F(x) = (x + 2)² - 3

Therefore, Option (C) will be the answer.