{"id":36,"date":"2014-10-16T23:19:06","date_gmt":"2014-10-16T23:19:06","guid":{"rendered":"https:\/\/blue-mathbelt.marjoriesayer.com\/?p=36"},"modified":"2014-10-17T14:38:31","modified_gmt":"2014-10-17T14:38:31","slug":"week-1-polynomials-day-4","status":"publish","type":"post","link":"https:\/\/blue-mathbelt.marjoriesayer.com\/?p=36","title":{"rendered":"Week 1: Polynomials &#8211; Day 4"},"content":{"rendered":"<p>Cubic polynomials.<\/p>\n<p>1. Sketch the graph of f(x) = x<sup>3<\/sup>.<\/p>\n<p>2. Sketch the graph of g(x) = x(x<sup>2<\/sup> + 1).<\/p>\n<p>Bonus questions: what is the difference between f(x) and g(x), in the neighborhood of x = 0? How many real roots do f(x) and g(x) have?<\/p>\n<p>3. Sketch the graph of h(x) = x(x &#8211; 3)<sup>2<\/sup>. Hint: how many real roots does h(x) have? What are the values of h(x) around and between the roots?<\/p>\n<p>4. Sketch the graph of p(x) = x(x &#8211; 1)(x &#8211; 2). Hint: how many real roots does p(x) have? What are the values of p(x) around and between the roots?<\/p>\n<p>5. Sketch the graph of q(x) = -x(x &#8211; 1)(x &#8211; 2).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Cubic polynomials. 1. Sketch the graph of f(x) = x3. 2. Sketch the graph of g(x) = x(x2 + 1). Bonus questions: what is the difference between f(x) and g(x), in the neighborhood of x = 0? How many real roots do f(x) and g(x) have? 3. Sketch the graph of h(x) = x(x &#8211; [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-36","post","type-post","status-publish","format-standard","hentry","category-polynomials"],"_links":{"self":[{"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/posts\/36","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=36"}],"version-history":[{"count":1,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/posts\/36\/revisions"}],"predecessor-version":[{"id":37,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=\/wp\/v2\/posts\/36\/revisions\/37"}],"wp:attachment":[{"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=36"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=36"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blue-mathbelt.marjoriesayer.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=36"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}