Given the equation y = x^2 + 3, what type of graph does it represent?

The equation y = x^2 + 3 represents a parabola because it is in the standard form of a quadratic function, which is typically written as y = ax^2 + bx + c. In this case, the leading coefficient (a) is 1, indicating that the parabola opens upwards. The constant term (c) is 3, which shifts the entire graph vertically upwards by 3 units.

Parabolas are characterized by their U-shaped curves, and this specific equation does not contain any linear (x) or higher-order terms, confirming that it is a simple quadratic function. Unlike other shapes such as lines, circles, or ellipses, a parabola displays symmetry about its vertex and can extend infinitely in the horizontal direction while curving upwards. This is why the correct identification of the graph represented by the equation is a parabola.