Converting a Semicircular Graph to Its Algebraic Function Representation

In this problem, we are tasked with identifying the algebraic representation of a function given a graphical depiction. Given the problem's indication that we are dealing with parabolas, particularly those of the form $y = x^2 + c$, we need to examine the provided graph for features typical of this family of functions.

The graph structure in the problem suggests a parabolic curve, centered symmetrically, which is indicative of the simplest unmodified parabola, $y = x^2$. The vertex likely lies at the origin, and the parabola opens upwards, a key characteristic of the function $y = x^2$ when the coefficient of $x^2$ is positive and equal to 1.

Upon reviewing the multiple-choice options, the expression that corresponds to this graph is:

• Option 1: $y = x^2$

Therefore, the algebraic representation that corresponds to the function is $y = x^2$.