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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.
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 \((h, k) .\)
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 the focus (and also from the origin to directrix) Example: Find the focus for the equation y 2 =5x.
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 vertex: h = − b /(2 a )
A parabola is the characteristic U-shaped curve of a quadratic equation. A parabola can be used to model many real-world phenomena. For example, when you shoot a basketball, the path of the ball creates a parabola.
Learning Objectives. In this section, you will: Graph parabolas with vertices at the origin. Write equations of parabolas in standard form. Graph parabolas with vertices not at the origin. Solve applied problems involving parabolas.
We introduce the vertex and axis of symmetry for a parabola and give a process for graphing parabolas. We also illustrate how to use completing the square to put the parabola into the form f(x)=a(x-h)^2+k.
Parabola: A parabola is all points in a plane that are the same distance from a fixed point and a fixed line. The fixed point is called the focus, and the fixed line is called the directrix of the parabola.
Equation of Parabola. Definition and Equation of a Parabola with Vertical Axis. A parabola is the set of all points M (x,y) M (x, y) in a plane such that the distance from M M to a fixed point F F called the focus is equal to the distance from M M to a fixed line called the directrix as shown below in the graph.
How to find the equation of a parabola using its vertex. We learn how to use the coordinates of a parabola's vertex (maximum, or minimum, point) to write its equation in vertex form in order to find the parabola's equation. The method is explained in detail with tutorials and a step-by-step method.