What is the equation of the blue graph?

Option C;
G(x)  = (x - 1)² - 3
This form of a quadratic equation is attained by 'completing the square';
This form tells us the coordinates of the vertex of a quadratic, i.e. the sole turning/stationary point or the highest/lowest point of the quadratic graph;
In general, for any quadratic that you complete the square with, you will get:
(x + a)² + b, for which the vertex is (-a, b).
In the case of G(x), we can see from the graph that the vertex (lowest point) is: (1, -3)
Therefore the completed the square form of the equation we want is going to be: (x - 1)² - 3.