{"id":862,"date":"2020-05-02T00:53:00","date_gmt":"2020-05-02T00:53:00","guid":{"rendered":"http:\/\/www.kyjee.com\/?p=862"},"modified":"2020-05-07T04:18:39","modified_gmt":"2020-05-07T04:18:39","slug":"introduction-to-quadratics","status":"publish","type":"post","link":"http:\/\/www.kyjee.com\/?p=862","title":{"rendered":"Introduction to Quadratics"},"content":{"rendered":"\n

What is a Quadratic Relation?<\/strong><\/p>\n\n\n\n

A quadratic relation is a non-linear relation, in which the second differences <\/em>are constant (and the first differences are not).  When the coordinates of a quadratic relation are plotted onto a graph, they can be connected to form a curved<\/em>, U-shaped line called a parabola.<\/em><\/p>\n\n\n\n

Second Differences!<\/strong><\/p>\n\n\n\n

To better understand the concept of quadratic relations, let\u2019s look at an example.<\/p>\n\n\n\n

Here we have a quadratic relation, set up in our standard table of values:<\/p>\n\n\n\n

x <\/em><\/strong><\/td>y<\/em><\/strong><\/td><\/tr>
1<\/td>0<\/td><\/tr>
2<\/td>2<\/td><\/tr>
3<\/td>6<\/td><\/tr>
4<\/td>12<\/td><\/tr>
5<\/td>20<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

You may be wondering, how would I know if this was a quadratic relation or not?<\/em><\/p>\n\n\n\n

  • We can identify if a relation is quadratic or not by examining second differences.  <\/li><\/ul>\n\n\n\n
    1. First, we must find the first<\/em> differences – <\/em>Remember, these are the differences between each of the y-values.\u00a0 We subtract a y-value by the value listed on the row above it to find its first difference (*this is how we find the first differences if the x-values increase\/decrease at a constant rate on the table of values).<\/li><\/ol>\n\n\n\n
      \"\"\/<\/figure>\n\n\n\n
      1. Now that we have found our first differences, we can find the second differences.\u00a0 Finding the second difference is like finding the first difference.\u00a0 We subtract a first difference value by the number listed on the row above it.<\/li><\/ol>\n\n\n\n
        \"\"\/<\/figure>\n\n\n\n

        Now, notice how the second differences are constant, <\/em>and the first differences are not.  This means that the relation showed in the table is quadratic! <\/p>\n\n\n\n

        (Remember: in a linear relation, the first differences are constant.)<\/p>\n\n\n\n

        Parabolas<\/strong><\/p>\n\n\n\n

        In a linear relation, the coordinates can be connected to form a line.<\/p>\n\n\n\n

        In a quadratic relation, the coordinates can be connected to form a curved, U-shaped line called a parabola.<\/p>\n\n\n\n

        \"\"\/<\/figure>\n\n\n\n

        Parabolas and Second Differences<\/strong><\/p>\n\n\n\n

        When the second differences are positive, the parabola opens upward.<\/p>\n\n\n\n

        When the second differences are negative, the parabola opens downward.<\/p>\n\n\n\n

        (When the second differences are 0, the relation is linear and there is no parabola because the first differences are equal.)<\/p>\n\n\n\n

        This is the first step in understanding quadratic relations!  Stay posted for more articles on quadratics and anything math-related!<\/p>\n","protected":false},"excerpt":{"rendered":"

        This article will introduce you to quadratic relations. It explains the concept of second differences and parabolas, as well as overviews some material from linear relations!<\/p>\n","protected":false},"author":3,"featured_media":863,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[17,12],"tags":[],"_links":{"self":[{"href":"http:\/\/www.kyjee.com\/index.php?rest_route=\/wp\/v2\/posts\/862"}],"collection":[{"href":"http:\/\/www.kyjee.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.kyjee.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.kyjee.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"http:\/\/www.kyjee.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=862"}],"version-history":[{"count":4,"href":"http:\/\/www.kyjee.com\/index.php?rest_route=\/wp\/v2\/posts\/862\/revisions"}],"predecessor-version":[{"id":937,"href":"http:\/\/www.kyjee.com\/index.php?rest_route=\/wp\/v2\/posts\/862\/revisions\/937"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.kyjee.com\/index.php?rest_route=\/wp\/v2\/media\/863"}],"wp:attachment":[{"href":"http:\/\/www.kyjee.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=862"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.kyjee.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=862"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.kyjee.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=862"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}