To solve the problem we will consider the red graph as the starting point. If we compare both graphs we can notice that they have the same shape, but are at different places of the coordinate plane, this means that there was a translation performed on the red graph to produce the blue one.
To perform a translation on a graph we need to add a constant into the equation that forms the graph. If we want to move the graph vertically we need to add the constant to the whole expression, while if we need to move the graph horizontally we need to add the constant to the argument (x) of the expression. With this in mind we can solve the question.
We can notice by looking at the blue graph that its vertice is on the coordinates (-2, -3), while originally it was at (0,0). So we need to add "3" to the argument and subtract "2" from the whole expression. This is shown below:
[tex]g(x)=(x+3)^2-2[/tex]
The expression for g(x) is (x+3)²-2
