Lesson Plan

Define a parabola as the locus of points equidistant from a fixed point (focus) and a fixed line (directrix)

Derive the equation of a parabola with vertex at the origin, focus at (0, p), and directrix y = -p, obtaining y = x^2/(4p)

Identify the focus, directrix, and vertex of a parabola from its equation in standard form

Write the equation of a parabola given its focus and directrix for both vertical and horizontal orientations

Connect the geometric definition of a parabola to the vertex form of a quadratic function y = a(x - h)^2 + k

HSG.GPE.A.2

HSG.GPE.A.2: Derive the equation of a parabola given a focus and directrix.