ANSWER
C. [tex]g(x) = {(x + 3)}^{2} - 2[/tex]
EXPLANATION
The blue graph is obtained by shifting the red to the left by 3 units and down 2 units.
The vertex is now at (-3,-2).
The base function has equation:
[tex]f(x) = {x}^{2} [/tex]
This implies that,
[tex]g(x) = f(x + 3) - 2[/tex]
[tex]g(x) = {(x + 3)}^{2} - 2[/tex]
The correct answer is C
