Which function is illustrated by a parabola that intersects at the origin?

The function represented by a parabola that intersects at the origin is quadratic in nature. Specifically, the equation ( y = x^2 ) is a classic example of a parabolic function. This type of function is symmetric about the y-axis and opens upward, with its vertex located at the origin (0, 0). When plotted, it creates a U-shaped curve that passes through the origin, which means that when ( x = 0 ), ( y ) also equals 0, confirming the intersection point at the origin.

The characteristic of a parabola not only helps to identify the graphical representation but also reflects its mathematical properties. The ( x^2 ) function generates positive outputs for all non-negative values of ( x ), reinforcing the idea that the graph rises on both sides of the vertex.

In contrast, the other functions do not produce a parabola that intersects the origin. For example, the function ( y = \sqrt{x} ) only produces real outputs for non-negative ( x ) and does not exist for negative values, meaning it will not create a parabola. The absolute value function ( y = |x| ) produces a V-shaped graph, also not a parabola, and it