A parabola as function of x.
y=ax2 + bx + c
a=1; b=2; c=0
a=1; b=0; c=0
a=1; b=-2; c=0
a=-0.5; b=0; c=5
a=4; b=0; c=-2
a=-0.2; b=-2; c=4
The Vertex of a Parabola
Vertex equation of a parabola:
y=a(x-h)2 + k
The vertex is the point: (h,k).
Focus of a Parabola
A parabola with the vertex at the origin (0,0), that is symmetric around the y-axis can be written as:
y = ax2;
The focus point is then defined as f = (0, 1/4a). The vertex is the point (0,0)
with a=1 we get the parabola: y = x2.
The focus is the point (0, 1/4).
Parabola: y=x2; focus = (0, 0.25); vertex = (0.0, 0.0).
General Construction of a Parabola
A parabola is a set of points that have the same distance between a given point the focus and a given line the base line.