Difference between revisions of "Parabola"
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== Parabola Equations == | == Parabola Equations == | ||
| − | There are several "standard" ways to write the equation of a parabola. The first is polynomial form: <math>y = a{x}^2+b{x}+c</math> where a, b, and c are | + | There are several "standard" ways to write the [[equation]] of a parabola. The first is [[polynomial]] form: <math>y = a{x}^2+b{x}+c</math> where a, b, and c are [[constant]]s. This is useful for manipulating the polynomial. |
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| + | The second is [[completing the square | completed square]] form, or <math>y=a(x-h)^2+k</math> where a, h, and k are constants and the [[vertex]] is (h,k). This is very useful for graphing the quadratic because the vertex and stretching factor are immediately before you. | ||
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| + | The third way is the conic section form, or <math>y^2</math><math>=4px</math> or <math>x^2=4py</math> where the p is a constant, and is the distance from the focus to the directrix. | ||
==Graphing Parabolas== | ==Graphing Parabolas== | ||
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| + | {{stub}} | ||
Revision as of 09:15, 24 June 2006
A parabola is a type of conic section. A parabola is a locus of points that are equidistant from a point (the focus) and a line (the directrix).
Parabola Equations
There are several "standard" ways to write the equation of a parabola. The first is polynomial form: 
where a, b, and c are constants. This is useful for manipulating the polynomial.
The second is completed square form, or 
where a, h, and k are constants and the vertex is (h,k). This is very useful for graphing the quadratic because the vertex and stretching factor are immediately before you.
The third way is the conic section form, or 
or 
where the p is a constant, and is the distance from the focus to the directrix.
Graphing Parabolas
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