{"id":2727,"date":"2020-01-07T13:13:00","date_gmt":"2020-01-07T12:13:00","guid":{"rendered":"http:\/\/jhmaths.fr\/?page_id=2727"},"modified":"2024-11-24T13:34:22","modified_gmt":"2024-11-24T12:34:22","slug":"second-degre","status":"publish","type":"page","link":"https:\/\/jhmaths.fr\/index.php\/premiere-technologique\/second-degre\/","title":{"rendered":""},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center\">Fonction du second degr\u00e9<\/h2>\n\n\n\n<figure class=\"wp-block-embed is-type-rich is-provider-prise-en-charge-des-contenus-embarqu-s wp-block-embed-prise-en-charge-des-contenus-embarqu-s wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Polyn\u00f4me du Second Degr\u00e9 2nde et Forme Canonique du Trin\u00f4me - Mathrix\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Slh5PcEnwHU?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p style=\"border-width:2px;border-radius:5px;padding-top:var(--wp--preset--spacing--20);padding-right:var(--wp--preset--spacing--20);padding-bottom:var(--wp--preset--spacing--20);padding-left:var(--wp--preset--spacing--20)\"><strong>D\u00e9finition :<\/strong> Une fonction du second degr\u00e9 s&rsquo;\u00e9crit \\(f(x)=ax^2+bx+c\\) o\u00f9 \\(a,b,c \\) sont trois nombres donn\u00e9s.<\/p>\n\n\n\n<p><strong>Exemples :<\/strong><\/p>\n\n\n\n<p>\\(x^2+4\\) (\\(a\\) vaut 1, \\(b\\) vaut 0 et \\(c\\) vaut 4)<br>\\(3x^2-2x+5\\) (\\(a\\) vaut 3, \\(b\\) vaut -2 et \\(c\\) vaut 5)<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><br>La parabole &#8211; \u00e9l\u00e9ments caract\u00e9ristiques<\/h2>\n\n\n\n<p style=\"border-width:2px;border-radius:5px;padding-top:var(--wp--preset--spacing--20);padding-right:var(--wp--preset--spacing--20);padding-bottom:var(--wp--preset--spacing--20);padding-left:var(--wp--preset--spacing--20)\">&nbsp;Une fonction du second degr\u00e9 \\(f : x \\mapsto ax^2+bx+c\\) est repr\u00e9sent\u00e9e sous la forme d&rsquo;une parabole, dont l&rsquo;orientation d\u00e9pend du signe de \\(a\\).<br>Cette parabole poss\u00e8de un <strong>axe de sym\u00e9trie vertical<\/strong> qui passe par son <strong>sommet<\/strong>.<\/p>\n\n\n\n<p><strong>Exemples :<\/strong><br><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>avec \\(a\\) n\u00e9gatif (il vaut -3), sommet \\(S(2;4)\\) et axe de sym\u00e9trie d&rsquo;\u00e9quation \\(x=2\\)<br><br><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/parabole-avec-elemts-carac-300x155.jpg\" alt=\"\"><br><\/li>\n\n\n\n<li>avec \\(a\\) positif (il vaut 4), sommet \\(S(1;1)\\) et axe de sym\u00e9trie d&rsquo;\u00e9quation \\(x=1\\)<br><br><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/parabole-avec-elemts-carac2-300x170.jpg\" alt=\"\"><\/li>\n<\/ul>\n\n\n\n<p>&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center\">Les 3 formes<\/h2>\n\n\n\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-container-core-group-is-layout-9e9be3cb wp-block-group-is-layout-constrained\" style=\"border-width:2px;border-radius:5px;padding-top:var(--wp--preset--spacing--20);padding-right:var(--wp--preset--spacing--20);padding-bottom:var(--wp--preset--spacing--20);padding-left:var(--wp--preset--spacing--20)\">\n<h3 class=\"wp-block-heading\">\\(f(x)=ax^2\\)<\/h3>\n\n\n\n<p>La parabole qui repr\u00e9sente \\(y=ax^2\\) passe par l&rsquo;origine et est :<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>tourn\u00e9e vers le haut si \\(a\\) est positif (courbes bleue et verte)<\/li>\n\n\n\n<li>tourn\u00e9e vers le bas si \\(a\\) est n\u00e9gatif (courbe rouge)<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"300\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/parabole-ax2-300x300.jpg\" alt=\"\" class=\"wp-image-3209\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/parabole-ax2-300x300.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/parabole-ax2-150x150.jpg 150w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/parabole-ax2-220x220.jpg 220w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/parabole-ax2.jpg 427w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-container-core-group-is-layout-9e9be3cb wp-block-group-is-layout-constrained\" style=\"border-width:2px;border-radius:5px;padding-top:var(--wp--preset--spacing--20);padding-right:var(--wp--preset--spacing--20);padding-bottom:var(--wp--preset--spacing--20);padding-left:var(--wp--preset--spacing--20)\">\n<h3 class=\"wp-block-heading\">\\(f(x)=ax^2+b\\)<\/h3>\n\n\n\n<p>La parabole qui repr\u00e9sente \\(y=ax^2+b\\) s&rsquo;obtient de la pr\u00e9c\u00e9dente par un d\u00e9calage vertical de \\(b\\) unit\u00e9s<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"249\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/parabole-ax2plusb-300x249.jpg\" alt=\"\" class=\"wp-image-3210\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/parabole-ax2plusb-300x249.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/parabole-ax2plusb.jpg 439w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-container-core-group-is-layout-9e9be3cb wp-block-group-is-layout-constrained\" style=\"border-width:2px;border-radius:5px;padding-top:var(--wp--preset--spacing--20);padding-right:var(--wp--preset--spacing--20);padding-bottom:var(--wp--preset--spacing--20);padding-left:var(--wp--preset--spacing--20)\">\n<h3 class=\"wp-block-heading\">\\(f(x)=a(x-x_1)(x-x_2)\\)<\/h3>\n\n\n\n<p>La parabole qui repr\u00e9sente \\(y=a(x-x_1)(x-x_2)\\) coupe l&rsquo;axe des abscisses aux valeurs \\(x_1\\) et \\(x_2\\) (appel\u00e9es <em>racines<\/em> de la fonction)<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"238\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/parabole-factorisee-300x238.jpg\" alt=\"\" class=\"wp-image-3211\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/parabole-factorisee-300x238.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/parabole-factorisee.jpg 445w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n<\/div>\n\n\n\n<div style=\"height:133px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\">\n<h2 class=\"wp-block-heading has-text-align-center\">Quizz<\/h2>\n\n\n\n<p>\\(P_1\\), \\(P_2\\), \\(P_3\\), \\(P_4\\) repr\u00e9sentent quatre fonctions polyn\u00f4mes de degr\u00e9 2.<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"280\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/quizz-paraboles-55-300x280.jpg\" alt=\"\" class=\"wp-image-3214\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/quizz-paraboles-55-300x280.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/quizz-paraboles-55-558x520.jpg 558w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2020\/10\/quizz-paraboles-55.jpg 645w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-55\" class=\"h5p-iframe\" data-content-id=\"55\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"1 Techno 2nd degr\u00e9 - parabole\"><\/iframe><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Fonction du second degr\u00e9 D\u00e9finition : Une fonction du second degr\u00e9 s&rsquo;\u00e9crit \\(f(x)=ax^2+bx+c\\) o\u00f9 \\(a,b,c \\) sont trois nombres donn\u00e9s. Exemples : \\(x^2+4\\) (\\(a\\) vaut 1, \\(b\\) vaut 0 et \\(c\\) vaut 4)\\(3x^2-2x+5\\) (\\(a\\) vaut 3, \\(b\\) vaut -2 et \\(c\\) vaut 5) La parabole &#8211; \u00e9l\u00e9ments caract\u00e9ristiques &nbsp;Une fonction du second degr\u00e9 \\(f : [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2319,"menu_order":11,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"folder":[],"class_list":["post-2727","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2727","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/comments?post=2727"}],"version-history":[{"count":35,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2727\/revisions"}],"predecessor-version":[{"id":3608,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2727\/revisions\/3608"}],"up":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/2319"}],"wp:attachment":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/media?parent=2727"}],"wp:term":[{"taxonomy":"folder","embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/folder?post=2727"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}