{"id":1538,"date":"2020-06-22T14:24:31","date_gmt":"2020-06-22T21:24:31","guid":{"rendered":"https:\/\/mathtalk.sdsu.edu\/wordpress\/?page_id=1538"},"modified":"2020-07-31T10:16:07","modified_gmt":"2020-07-31T17:16:07","slug":"parabolas-lesson-10-teachers","status":"publish","type":"page","link":"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-10-teachers\/","title":{"rendered":"Parabolas Lesson 10 (Teachers)"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Getting and Using Geometric Information<\/h3>\n\n\n\n<p>Given the equation of a parabola in any form, Sasha and Keoni find geometric information (such as the focus, directrix, p-value, and vertex) about the parabola.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-10-teachers\/parabolas-lesson-10-episode-1-teachers\/\">Episode 1: Making Sense<\/a><\/h5>\n\n\n\n<p>Keoni and Sasha begin to find geometric information from the equation, y = (x\u20132.4)<sup>2<\/sup>\/6, in vertex form. They find the p-value and determine the vertex of the parabola.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-10-teachers\/parabolas-lesson-10-episode-2-teachers\/\">Episode 2: Exploring<\/a><\/h5>\n\n\n\n<p>Sasha and Keoni graph the equation y = (x\u20132.4)<sup>2<\/sup>\/6. They determine the coordinates of the focus and the equation of the directrix from the geometric information in the equation.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-10-teachers\/parabolas-lesson-10-episode-3-teachers\/\">Episode 3: Repeating Your Reasoning<\/a><\/h5>\n\n\n\n<p>Keoni and Sasha look for geometric information of a parabola represented by the equation y = 2(x \u2013 3)<sup>2<\/sup> + 1. They start by finding the vertex and the p-value.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-10-teachers\/parabolas-lesson-10-episode-4-teachers\/\">Episode 4: Making Sense<\/a><\/h5>\n\n\n\n<p>Keoni and Sasha examine an equation of a parabola in a different form, y = x<sup>2<\/sup> \u2013 4x + 4. When they look for geometric information, the p-value and vertex are not apparent. They start by rewriting the equation.<\/p>\n\n\n\n<h5 class=\"wp-block-heading\"><a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/parabolas-unit-teachers\/parabolas-lesson-10-teachers\/parabolas-lesson-10-episode-5-teachers\/\">Episode 5: Exploring<\/a><\/h5>\n\n\n\n<p>Sasha and Keoni examine yet another equation of a parabola that is not in vertex form, y = x<sup>2<\/sup> \u2013 4x + 5. They start out by seeking a method to re-express the equation in vertex form.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-background has-vivid-cyan-blue-background-color has-vivid-cyan-blue-color\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Mathematics in this Lesson <a href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/parabolas-teacher-docs\/parabolas-l10-mathematics-in-this-lesson.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><img loading=\"lazy\" decoding=\"async\" width=\"34\" height=\"34\" class=\"wp-image-2214\" style=\"width: 34px; vertical-align: middle;\" src=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-content\/uploads\/2020\/07\/pdf.jpg\" alt=\"\"><\/a><\/h3>\n\n\n\n<p class=\"has-medium-font-size\">Targeted Understandings <input type='hidden' bg_collapse_expand='69ef1d42441ba2035380659' value='69ef1d42441ba2035380659'><input type='hidden' id='bg-show-more-text-69ef1d42441ba2035380659' value=' '><input type='hidden' id='bg-show-less-text-69ef1d42441ba2035380659' value=' '><button id='bg-showmore-action-69ef1d42441ba2035380659' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69ef1d42441ba2035380659' ><\/p>\n\n\n\n<p>This lesson can help students:<\/p>\n\n\n\n<p>1. Understand that when the equation representing a parabola is written in vertex form [y = (x\u2013h)<sup>2<\/sup>\/(4p) + k], then the vertex can be easily determined as (h ,k) and the p-value can located in the denominator and can be used, along with the vertex, to determine the focus and directrix of the parabola.<\/p>\n\n\n\n<p>2. Understand that geometric information (e.g., the vertex, p-value, focus, and directrix) can also be located from a parabola that is given in a different form, by first re-expressing the equation in an equivalent vertex form. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Common Core Math Standards <input type='hidden' bg_collapse_expand='69ef1d42442665044654913' value='69ef1d42442665044654913'><input type='hidden' id='bg-show-more-text-69ef1d42442665044654913' value=' '><input type='hidden' id='bg-show-less-text-69ef1d42442665044654913' value=' '><button id='bg-showmore-action-69ef1d42442665044654913' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69ef1d42442665044654913' ><\/p>\n\n\n\n<p><a href=\"http:\/\/www.corestandards.org\/Math\/Content\/HSF\/IF\/C\/8\/\"><strong>CCSS.M.HSF.IF.C.8<\/strong><\/a>. <em>Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.<\/em><\/p>\n\n\n\n<p>In this lesson, Sasha and Keoni re-express quadratic functions like y = 2(x \u2013 3)<sup>2<\/sup> + 1 and y = x<sup>2<\/sup> \u2013 4x + 4 in vertex form [y = (x\u2013h)<sup>2<\/sup>\/(4p) + k] in order to locate geometric information about the graphs (such as the vertex, p-value, focus and directrix). To rewrite the function y = 2(x \u2013 3)<sup>2<\/sup> + 1 in vertex form, they think of 2 as 1 divided by \u00bd [see <strong>2:20 \u2013 2:31<\/strong> in <strong>Episode 3<\/strong>] and \u00bd as 4 multiplied by 1\/8 [<strong>3:21 \u2013 3:43, Episode 3<\/strong>]. To rewrite the function y = x<sup>2<\/sup> \u2013 4x + 4 in vertex form, Sasha and Keoni figure out that they need to factor, but that not every way of factoring is helpful. For example, factoring out the x from x<sup>2<\/sup> \u2013 4x yields y = x(x \u2013 4) + 4 [1<strong>:06 \u2013 1:30, Episode 4<\/strong>], which doesn\u2019t help them. However, factoring the entire trinomial yields y = (x \u2013 2)<sup>2<\/sup>, which is very close to being in vertex form [<strong>3:14 \u2013 2:52, Episode 4<\/strong>]. <\/div><\/p>\n\n\n\n<p class=\"has-medium-font-size\">Common Core Math Practices <input type='hidden' bg_collapse_expand='69ef1d424431a0019174264' value='69ef1d424431a0019174264'><input type='hidden' id='bg-show-more-text-69ef1d424431a0019174264' value=' '><input type='hidden' id='bg-show-less-text-69ef1d424431a0019174264' value=' '><button id='bg-showmore-action-69ef1d424431a0019174264' class='bg-showmore-plg-button bg-blue-button bg-arrow '   style=\" color:white;\"> <\/button><div id='bg-showmore-hidden-69ef1d424431a0019174264' ><\/p>\n\n\n\n<p><a href=\"http:\/\/www.corestandards.org\/Math\/Practice\/MP1\/\">CCSS.Math.Practice.MP1<\/a>: Make sense of problems and persevere in solving them.<\/p>\n\n\n\n<p>An important aspect of Math Practice 1 is not giving up, even when several attempts have not been fruitful. In Episode 5, Sasha and Keoni face a challenging task of rewriting y = x<sup>2<\/sup> \u2013 4x + 5 in vertex form. They begin with a false start, as Keoni incorrectly factors x<sup>2<\/sup> \u2013 4x + 5 as (x \u2013 5)(x + 1) [<strong>1:08 \u2013 1:44, Episode 5<\/strong>]. Instead of getting discouraged, Keoni tells Sasha, \u201cLet\u2019s not give up\u201d [<strong>2:19 \u2013 2:26<\/strong>]. And they don\u2019t! Sasha tries factoring out the x [<strong>2:53 \u2013 3:07<\/strong>], which doesn\u2019t end up helping. However, when they explain the correspondences between y = x<sup>2<\/sup> \u2013 4x + 5 and the function they worked with in <strong>Episode 4<\/strong> [y = x<sup>2<\/sup> \u2013 4x + 4], they are able to successfully rewrite the given equation as y = (x \u2013 2)<sup>2<\/sup> + 1 [<strong>4:25 \u2013 4:46<\/strong>]. <\/div><\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/\" style=\"background-color:#2d4059\">Home<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/mathtalk-for-teachers\/\" style=\"background-color:#2d4059\">Teachers Home<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background\" href=\"https:\/\/mathtalk.sdsu.edu\/wordpress\/parabolas-unit-teachers\/\" style=\"background-color:#2d4059\">Parabolas<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Getting and Using Geometric Information Given the equation of a parabola in any form, Sasha and Keoni find geometric information (such as the focus, directrix, p-value, and vertex) about the parabola. Episode 1: Making Sense Keoni and Sasha begin to find geometric information from the equation, y = (x\u20132.4)2\/6, in vertex form. They find the [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":543,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1538","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1538","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/comments?post=1538"}],"version-history":[{"count":9,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1538\/revisions"}],"predecessor-version":[{"id":2250,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/1538\/revisions\/2250"}],"up":[{"embeddable":true,"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/pages\/543"}],"wp:attachment":[{"href":"https:\/\/mathtalk.sdsu.edu\/wordpress\/wp-json\/wp\/v2\/media?parent=1538"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}