MC 2 Study Guide - Final Guide: Completing The Square, Sketchpad, Cartesian Coordinate System

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20 Nov 2021

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A parabola is the locus of points equidistant from a point (focus) and line (directrix). Let (x, y) be on the above parabola. X2 + y2 2yp + p2 = y2 + 2yp + p2. 4p: for the parabola y = ax2, we have vertex at the origin. We have thus con rmed the equality of the forms y = ax2 and y = 1. 4p: (here we will actually write up #4 - more speci cally, we will generalize the p-form of a parabola with vertex at (h, k) rather than the origin. ) First, given a parabola centered at the origin, we translate by k units upward to a parabola with vertex (0, k). x2. Next, we translate in the x-direction by h units: y = ax2 + k y = a(x h)2 + k. This last equation is the familiar vertex form of a parabola. Observe that a remains the same: (we here write up #3).

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