What is a key characteristic of the parabola in relation to its vertex?

The choice highlighting that a parabola opens upwards if the leading coefficient is positive is a fundamental property of quadratic functions. A parabola is defined by the equation of the form (y = ax^2 + bx + c), where (a) is the leading coefficient.

When (a > 0), the arms of the parabola extend upwards, creating a "U" shape, with the vertex being the lowest point on the graph. This behavior is crucial because it indicates the nature of the quadratic function's graph and helps in determining the direction of the parabola. Conversely, if the leading coefficient is negative, the parabola opens downwards, forming an inverted "U" shape, positioning the vertex as the highest point.

Understanding this characteristic is vital for analyzing the graph of a quadratic function, as it not only informs the shape but also assists in solving various mathematical problems related to quadratics, such as finding maximum or minimum values.