http://www.ck12.org Chapter 9. Conics
Notice how the three pointsP 1 ,P 2 ,P 3 are each connected by a blue line to the focus pointFand the directrix lineL.
F P 1 =P 1 Q 1
F P 2 =P 2 Q 2
F P 3 =P 3 Q 3
There are two graphing equations for parabolas that will be used in this concept. The only difference is one equation
graphs parabolas opening vertically and one equation graphs parabolas opening horizontally. You can recognize
the parabolas opening vertically because they have anx^2 term. Likewise, parabolas opening horizontally have a
y^2 term. The general equation for a parabola opening vertically is(x−h)^2 =± 4 p(y−k). The general equation for
a parabola opening horizontally is(y−k)^2 =± 4 p(x−h).
Note that the vertex is still(h,k). The parabola opens upwards or to the right if the 4pis positive. The parabola
opens down or to the left if the 4pis negative. The focus is just a point that is distancepaway from the vertex. The
directrix is just a line that is distancepaway from the vertex in the opposite direction. You can sketch how wide the
parabola is by noting the focal width is| 4 p|.
Once you put the parabola into this graphing form you can sketch the parabola by plotting the vertex, identifyingp
and plotting the focus and directrix and lastly determining the focal width and sketching the curve.