What is the general form of a parabola equation?

The general form of a parabola equation is expressed as (y = ax^2 + bx + c). In this equation, (a), (b), and (c) are constants, where (a) determines the direction and width of the parabola. If (a) is positive, the parabola opens upwards, and if (a) is negative, it opens downwards. The (x^2) term indicates that this is a quadratic equation, which is essential for defining a parabolic curve. The presence of the linear term (bx) and the constant term (c) allows for the parabola to be positioned anywhere on the Cartesian plane.

The other options presented do not represent a parabola. For instance, the reciprocal function (y = k/x) shows hyperbolic characteristics rather than parabolic. The linear equations (y = ax + b) and (y = mx + b) describe straight lines, not curves, indicating either a constant slope or a linear relationship between (x) and (y). These forms lack the quadratic term necessary to shape a parabola, which is why they don’t fit the criteria needed to define a