Table of Contents
Definition and Equation of Parabola
A parabola is a mathematical curve that is shaped like an upside down U. The equation of a parabola is y = ax2, where a is the coefficient of x2. The graph of a parabola is symmetrical about the y-axis.
Parabolic Equation
The parabolic equation is a second order linear differential equation. It can be written in the form
y” + p(x)y’ + q(x)y = 0
where y is a function of x and p(x) and q(x) are constants. The graph of a solution to the parabolic equation is a parabola.
The Formula for Equation of a Parabola
The equation of a parabola with vertex at (h, k) and focus at (f, g) is y = a(x − h)2 + k.
Spot the Parabola at a Stroke
In mathematics, a parabola is a U-shaped curve. It is a conic section, formed by the intersection of a plane and a cone. The plane can be vertical or horizontal. The cone can be a right cone or a oblique cone. The vertex of the cone is the point where the plane intersects the cone. The axis of the cone is the line joining the vertex to the center of the base of the cone. The focal point of the parabola is the point where the axis of the cone intersects the parabola.
The standard equation of a parabola is y = x2. This equation can be used to find the coordinates of the vertex, the axis of the cone, and the focal point of the parabola.
To find the vertex of the parabola, use the equation to solve for x. The x-coordinate of the vertex is the root of the equation.
To find the axis of the cone, use the equation to solve for y. The y-coordinate of the axis of the cone is the root of the equation.
To find the focal point of the parabola, use the equation to solve for y. The y-coordinate of the focal point is the positive square root of the equation.
Usefulness of Parabola
A parabola is a curve in mathematics that is shaped like a U. It has two focal points, which are the points where the curve is the steepest. The parabola is often used in physics and engineering to model the path of a projectile. It can also be used to model the path of a light ray.
The Equation for Parabola in Standard Form
The equation for a parabola in standard form is y = ax^2 + bx + c. The a represents the y-intercept, the b represents the slope of the parabola, and the c represents the vertex of the parabola.
The Equation for Parabola in Vertex Form
The equation for a parabola in vertex form is y = a(x – h)2 + k. This equation can be used to find the vertex of a parabola, as well as the coordinates of the points on the parabola.
