Writing the Equation of Parabolas - Softschools.com
To write the equation of a parabola.... 1. Determine which pattern to use (based on whether it is horizontal or vertical) 2. Substitute in h and k. 3. Choose a coordinate to substitute in and …
Parabola - Formula, Graphing, Examples | Parabola Equation
The general equation of a parabola is: y = a (x-h) 2 + k or x = a (y-k) 2 +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y 2 = 4ax. Some of the important terms …
What are parabolas, their equations, their rules? | Purplemath
The general form of a parabola's equation is converted into the vertex form by completing the square — or by using the following formula to get the value of h, being the x-coordinate of the …
5.2: The Equation of the Parabola - Mathematics LibreTexts
A parabola is defined as the locus (or collection) of points equidistant from a given point (the focus) and a given line (the directrix). Another important point is the vertex or turning point of …
8.4: The Parabola - Mathematics LibreTexts
How to: Given its focus and directrix, write the equation for a parabola in standard form. Determine whether the axis of symmetry is the \(x\)- or \(y\)-axis. If the given coordinates of the …
Equation of a parabola from focus & directrix - Khan Academy
Given the focus (h,k) and the directrix y=mx+b, the equation for a parabola is (y - mx - b)^2 / (m^2 +1) = (x - h)^2 + (y - k)^2. Equivalently, you could put it in general form: x^2 + 2mxy + m^2 y^2 …
Parabola - Math is Fun
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: y 2 = 4ax. where a is the distance from the origin to …