Sasha and Keoni develop the vertex form of the equation of a parabola as y = (x\u2013h)2<\/sup>\/(4p) + k where the (h,k) is the vertex and p the distance from the vertex to the focus.<\/p>\n\n\n\n Sasha and Keoni examine the different equations they derived for parabolas with a p-value of 3 and a vertex not at the origin. By noticing patterns between the location of the vertex and the equation for the parabola, they make a prediction for the general equation of a parabola with a vertex at (h, k) and an unknown p-value.<\/p>\n\n\n\n Keoni and Sasha use the Pythagorean Theorem and the definition of a parabola to derive an equation of parabola with a p-value of 5 and a vertex at (9, 13).<\/p>\n\n\n\n Keoni and Sasha use the applet to explore the graphs of parabolas with a vertex at (9, 13) and an unknown p-value. Sasha and Keoni determine how to represent the coordinates of the focus and the equation of the directrix when p can take on any value.<\/p>\n\n\n\n Sasha and Keoni extend their work from the last episode to derive the equation of a family of parabolas that have a vertex at (9, 13).<\/p>\n\n\n\n Sasha and Keoni look back on their work with a parabola with a p-value of 5 and a vertex of (9, 13). By reflecting on their work and the equation y = (x \u2013 9)2<\/sup>\/(4p) + 13, they see 13 their graph.<\/p>\n\n\n\n Sasha and Keoni build on what they have learned in the previous episodes to begin to develop the general equation for any parabola with vertex (h, k) and the distance p from the vertex to the focus.<\/p>\n\n\n\n In the last episode Sasha and Keoni determined the distances of the sides of a right triangle on a general parabola with vertex (h, k) and distance p from the vertex to the focus. Next they derive the equation for the parabola by substituting those distances into the Pythagorean Theorem.<\/p>\n\n\n\nEpisode 1: Making Sense<\/a><\/h5>\n\n\n\n
Episode 2: Exploring<\/a><\/h5>\n\n\n\n
Episode 3: Making Sense<\/a><\/h5>\n\n\n\n
Episode 4: Exploring<\/a><\/h5>\n\n\n\n
Episode 5: Reflecting<\/a><\/h5>\n\n\n\n
Episode 6: Making Sense<\/a><\/h5>\n\n\n\n
Episode 7: Exploring<\/a><\/h5>\n\n\n\n