Final answer:
The function f(x)=1/2(x+2)^2-3 is a quadratic function that has been shifted to the left and downwards compared to the parent function y = x^2.
Step-by-step explanation:
The function f(x) = 1/2(x+2)^2-3 is a quadratic function that has been shifted to the left and downwards compared to the parent function y = x^2. The parent function y = x^2 is a simple parabola that opens upward with its vertex at the origin (0,0).
The function f(x) = 1/2(x+2)^2-3 is a parabola that also opens upward, but its vertex has been shifted to the left by 2 units and downwards by 3 units. This means that the vertex of f(x) is at the point (-2,-3).
By comparing the two functions, we can see that f(x) is wider than the parent function y = x^2, as the coefficient of x^2 in f(x) is smaller (1/2) compared to 1 in the parent function. Additionally, the graph of f(x) has been translated to the left and downwards compared to the parent function.