Ch10.2 and additional material Parabolas Ch10.2 and additional material

Conic Sections - Parabola The latus rectum is the line segment passing through the focus, perpendicular to the axis of symmetry with endpoints on the parabola. Latus Rectum Focus Vertex (h, k)

Conic Sections - Parabola The length of the latus rectum is 1/|a| The focal length is c=1/(4|a|) Latus Rectum Focus Focal length (c) Vertex (h, k)

Table of Rules : y = a(x - h)2 + k Opens Up Down Vertex (h,k) Axis x=h Focal length Focus (h, k+c) (h, k-c) Directrix y=k-c y=k+c Latus Rectum 4c

Table of Rules : x = a(y - k)2 + h Opens Right Left Vertex (h,k) Axis y=k Focal length Focus (h+c, k) (h-c, k) Directrix x=h-c x=h+c Latus Rectum 4c

Ex) Find the vertex, axis of symmetry and direction of opening.

Ex) Graph

Ex) Find the min/max value, the length of the latus rectum, and intercepts on the axis perpendicular to the axis of symmetry.