Difference between revisions of "Parabola"
Quantum leap (talk | contribs) m (changed "vertex" to "focus", edited completed square formula) |
IntrepidMath (talk | contribs) |
||
| Line 3: | Line 3: | ||
== 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 constants. The second is 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). 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. | + | 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 constants. This is useful for manipulation the polynomial. The second is 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 is immediately before you. 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== | ||
Revision as of 22:55, 19 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 manipulation 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 is 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.
