Presentation on theme: "Armando Martinez-Cruz Garrett Delk Department of Mathematics CSU Fullerton Presented at 2013."— Presentation transcript:
Armando Martinez-Cruz Amartinezfirstname.lastname@example.org Garrett Delk email@example.com Department of Mathematics CSU Fullerton Presented at 2013 CMC Conference Palm Springs, CA Parabolas and Quadratic Equations
Agenda Welcome CCSS Intro to Software Parabolas - Locus Sliders Questions
Parabolas and CCSS Mathematics » High School: Geometry » Expressing Geometric Properties with Equations Translate between the geometric description and the equation for a conic section CCSS.Math.Content.HSG-GPE.A.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. CCSS.Math.Content.HSG-GPE.A.1 CCSS.Math.Content.HSG-GPE.A.2 Derive the equation of a parabola given a focus and directrix. CCSS.Math.Content.HSG-GPE.A.2
Introduction to Software Points Segments Midpoint Perpendicular Lines Locus Sliders
Parabolas as a Locus The parabola is the locus of all points (x, y) that are equidistant to a fixed line called the directrix, and a fixed point called the focus.
Steps to Construct the Parabola-Locus Construct a point, A. This is the focus. Construct line BC (not through A). This is the directrix. Construct point D (different from A and B) on the directrix. Construct the perpendicular line to the directrix through D. Construct segment AD. Construct the midpoint, E, of segment AD. Construct the perpendicular bisector of segment AD. Construct the point of intersection, F, of this perpendicular bisector with the perpendicular to the directrix. Construct the locus of F when D moves along the directrix.