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- In mathematics, a parabola is a two-dimensional curve that is the graph of a quadratic equation. It has a distinct U-shaped appearance. The term "parabola" is derived from the Greek word "parabolas," which means "to throw."
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What is a parabola? It is geometrically defined by a set of points or locus of points that are equidistant from a point (the focus) and a line (the directrix). Parabolas can be found in many places in everyday life. A few examples are shown below. Can you guess where the focus point should be in the flash light or the satellite dish?
There we discovered that the graph of a quadratic equation (a polynomial of degree 2) is a parabola. We just learned that a parabola focuses into one point, everything that hits it straight on.
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- Components of Parabola
- Different Equations For Parabola
- Types of Parabola
- Graph of Parabola and Properties
- Application of Parabola
- Parabola in Conic Section
- Solved Example of A Parabola
Figure 1 – Components of Parabola The components of the parabola are illustrated in the figure above. 1. Axis of symmetry: The line that splits the parabola into two identical halves is known as the axis of symmetry. The directrix and the axis of symmetry are always perpendicular. 2. Vertex: The parabola’s highest or lowest point is known as the ve...
There are several different forms of the equation of a parabola that can be used, depending on the specific needs of the problem at hand. 1. Standard form: y = a(x – l)2+ m, where (l, m) denotes the vertex of the parabola. 2. In Vertex form: y = a(x – l)2, where (l, k) denotes the vertex of the parabola. This form is useful when the focus of the pa...
There are two main types of parabolas: those that open upwards and those that open downwards.These types are illustrated in the figure shown below. 1. A mathematical equation of the form y = ax2 + bx + c, where a > 0, defines an upward-openingparabola. This equation’s graph will be a parabola with an upward opening and a vertex at the bottom of the...
The graph of a parabola has several important features. Figure 4 – Graph of Parabola 1. The vertex is either the highest point on the curve or its lowestpoint, depending on how the parabola opens. It is situated at the coordinates (h, k), where h and k represent the x- and y-values, respectively. 2. The axis of symmetry is the line that divides the...
Parabolas have a wide range of applicationsin various fields, including mathematics, science, engineering, and technology. Here are a few examples: 1. Mathematicians use parabolas to represent and examine a wide range of phenomena, including the trajectory of a bullet and the power of sound waves. 2. In physics, parabolas are used to explain how ob...
A parabola is a particular kind of conic section, a curve created by the intersection of a right circular cone and a plane. The ellipse, hyperbola, and circle are the other shapesthat can have conic sections. A parabola is the collection of all points that are equidistant from a particular point (the focus) and a particular line (the directrix). It...
Example
Locate the parabola’s vertex according to the equation given by y = x2+ 2x – 3.
Solution
To find the vertex of the parabola, we can rewrite the equation in vertex form: y = a(x – h)2+ k. To do this, we can complete the square: y = x2 + 2x – 3 = (x2 + 2x) – 3 = x2 + 2x + 1 – 4 = (x + 1)2– 3 So, the vertex of the parabola is at the point (h,k) = (-1, -3). All mathematical drawings and images were created with GeoGebra.
Definition. A parabola is a curve where any point is at an equal distance from: a fixed point (the focus), and; a fixed straight line (the directrix)
What Is a Parabola? The section of a right circular cone by a plane parallel to a generator of the cone is a parabola. It is a locus of a point, which moves so that the distance from a fixed point (focus) is equal to the distance from a fixed line (directrix).
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What is a parabola. The precise parabola definition is: a collection of points such that the distance from each point on the curve to a fixed point (the focus) and a fixed straight line (the directrix) is equal. Parts of a parabola. The figure below shows the various parts of a parabola as well as some important terms.
