Editing Bézier curve (section)

===Second-order curve is a parabolic segment===
[[File:Quadratic_Bezier_parabola_equivalence.svg|thumb|upright|Equivalence of a quadratic Bézier curve and a parabolic segment]]

A quadratic Bézier curve is also a segment of a [[parabola]]. As a parabola is a [[conic section]], some sources refer to quadratic Béziers as "conic arcs".<ref name=freetype/> With reference to the figure on the right, the important features of the parabola can be derived as follows:<ref>{{cite book |author=Duncan Marsh |title=Applied Geometry for Computer Graphics and CAD |series=Springer Undergraduate Mathematics Series |edition=2nd |date=2005 |isbn=978-1-85233-801-5 |id={{ASIN|1852338016|country=uk}}}}</ref>

# Tangents to the parabola at the endpoints of the curve (A and B) intersect at its control point (C).
# If D is the midpoint of AB, the tangent to the curve which is [[perpendicular]] to CD (dashed cyan line) defines its vertex (V). Its axis of symmetry (dash-dot cyan) passes through V and is perpendicular to the tangent.
# E is either point on the curve with a tangent at 45° to CD (dashed green). If G is the intersection of this tangent and the axis, the line passing through G and perpendicular to CD is the directrix (solid green).
# The focus (F) is at the intersection of the axis and a line passing through E and perpendicular to CD (dotted yellow). The latus rectum is the line segment within the curve (solid yellow).