A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point and a fixed line. Its general equation is of the form y^2 = 4ax (if it opens left/right) or of the form …

Parabola with axis parallel to y -axis; p is the semi-latus rectum In Cartesian coordinates, if the vertex ⁠ ⁠ is the origin and the directrix has the equation , then, by examining the case , the focus ⁠ ⁠ is on the …

A parabola is a particular type of geometrical curve which, algebraically, corresponds to a quadratic equation. In geometrical terms, the parabola corresponds to the edge of slice of an inverted cone; …

Like the circle, the parabola is a quadratic relation, but unlike the circle, either x will be squared or y will be squared, but not both. You worked with parabolas in Algebra 1 when you graphed quadratic …

Jan 1, 2026 · The graph of a parabola can change position, direction, and width based on the coefficients of x 2 and x as well as the constant. Because those pieces of the equation are so …

Jul 23, 2025 · A parabola has four standard equations based on the orientation of the parabola and its axis. Each parabola has a different transverse axis and conjugated axis.

So the parabola is a conic section (a section of a cone). The simplest equation for a parabola is y = x2. Turned on its side it becomes y2 = x. (or y = √x for just the top half) A little more generally: where a is …

Explore equation and definition of a parabola through examples with detailed solutions and an intercative app. Examples, exercises and interactive activities are included.

From this equation, we can determine that the vertex of the parabola is at (1, 4), and the axis of symmetry is at x = 1. Once we know the vertex, we can plug in a few x-values on either side of the …

Jun 9, 2025 · Real-world situations can be modeled using the standard equations of parabolas. For instance, given the diameter and focus of a cross-section of a parabolic reflector, we can find an …