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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 below are helpful to understand the features and parts of a parabola y 2 = 4ax.
- Focus
Example 1: Find the equation of a parabola having the focus...
- Eccentricity of Parabola
Example 2: Determine the eccentricity of parabola if a = 8...
- Locus
The above equation can be converted to the form \(\dfrac{x^2...
- Focus
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 -2[h(m^2 - 1) +mb]x -2[k(m^2 + 1)^2 -b]y + (h^2 + k^2)(m^2 + 1) - b^2 = 0
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 the parabola. If the equation of a parabola is given in standard form then the vertex will be \((h, k) .\)
f(x) = ax2 + bx + c. where a, b, and c are real numbers and a ≠ 0. If a > 0, the parabola opens upward. If a < 0, the parabola opens downward. We can use the general form of a parabola to find the equation for the axis of symmetry.
The equations of parabolas with vertex (0, 0) (0, 0) are y 2 = 4 p x y 2 = 4 p x when the x-axis is the axis of symmetry and x 2 = 4 p y x 2 = 4 p y when the y-axis is the axis of symmetry. These standard forms are given below, along with their general graphs and key features.
Course: Algebra 1. > Vertex & axis of symmetry of a parabola. Google Classroom. About. Transcript. Sal rewrites a quadratic equation in vertex form and shows how it reveals the vertex of the corresponding parabola. Created by Sal Khan and Monterey Institute for Technology and Education. Questions. Tips & Thanks. Want to join the conversation?
The standard form of a parabola with vertex \((0,0)\) and the y-axis as its axis of symmetry can be used to graph the parabola. If \(p>0\), the parabola opens up. If \(p<0\), the parabola opens down.
