Equation of Parabola Equation of Parabola This is an applet to explore the equation of a parabola and its properties. The equation used is the standard equation that has the form (y - k)2 = 4a(x – h) where h and k are the x- and y-coordinates of the vertex of the parabola and a is a non zero real number (in this investigation we consider only cases with positive a). For the definition and construction of a parabola Go here. Examples of applications of the parabolic shape as Parabolic Reflectors and Antennas and a tutorial on how to Find The Focus of Parabolic Dish Antennas and on How Parabolic Dish Antennas work? are included in this site. The exploration is carried out by changing the parameters h, k and a included in the above equation. Follow the steps in the tutorial below. For similar tutorials on circle , Ellipse and the hyperbola can be found in this site.
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Standard Form Equation The standard form of a parabola's equation is generally expressed: 1. y = ax 2 + bx + c The role of 'a' If a> 0, the parabola opens upwards if a< 0, it opens downwards. The axis of symmetry The axis of symmetry is the line x = -b/2a Vertex Form of Equation The vertex form of a parabola's equation is generally expressed as : y= a(x-h)2+k 1. (h,k) is the vertex as you can see in the picture below 2. If a is positive then the parabola opens upwards like a regular "U". 3. If a is negative, then the graph opens downwards like an upside down "U". A. If |a| > 1, the graph of the parabola widens. This just means that the "U" shape of parabola stretches out sideways . B. If |a| < 1, the graph of the graph becomes narrower(The effect is the opposite of |a| > 1). In mathematics, a parabola ( /pəˈræbələ/; plural parabolae or parabolas, from the Greek παραβολή) is a conic section, created from the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface. Another way to generate a parabola is to examine a point (the focus) and a line (the directrix) on a plane. The locus of points in that plane that are equidistant from both the line and point is a parabola.
Learn More :- Equation for a parabola
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The line perpendicular to the directrix and passing through the focus (that is, the line that splits the parabola through the middle) is called the "axis of symmetry". The point on the axis of symmetry that intersects the parabola is called the "vertex", and it is the point where the curvature is greatest. Parabolas can open up, down, left, right, or in some other arbitrary direction. Any parabola can be repositioned and rescaled to fit exactly on any other parabola — that is, all parabolas are similar. The parabola has many important applications, from automobile headlight reflectors to the design of ballistic missiles. They are frequently used in physics, engineering, and many other areas.
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