{"id":8524,"date":"2021-11-09T14:35:50","date_gmt":"2021-11-09T13:35:50","guid":{"rendered":"https:\/\/mathsguyon.fr\/?page_id=8524"},"modified":"2021-11-09T15:36:50","modified_gmt":"2021-11-09T14:36:50","slug":"exercices-second-degre-2","status":"publish","type":"page","link":"https:\/\/mathsguyon.fr\/?page_id=8524","title":{"rendered":"Exercices second degr\u00e9"},"content":{"rendered":"

Exercice 1 :\u00a0<\/strong>Correction en vid\u00e9o<\/a><\/h2>\n

Soit $f$ la fonction d\u00e9finie sur $\\mathbb R$ par $f (x) = 2(x +3)^2 -2$<\/p>\n

1. D\u00e9terminer la forme d\u00e9velopp\u00e9e de $f$<\/p>\n

2. R\u00e9soudre, sans utiliser le discriminant :<\/p>\n

a. $f (x) = 6$<\/p>\n

b.$f (x) = 16$<\/p>\n

Exercice 2 :\u00a0<\/strong>Correction en vid\u00e9o<\/a><\/h2>\n

D\u00e9terminer par la m\u00e9thode alg\u00e9brique la forme canonique de la fonction $f$ d\u00e9finie sur $\\mathbb{R}$ par $f (x) = 3x^2 +6x +5$<\/p>\n

Exercice 3 :\u00a0<\/strong>Correction en vid\u00e9o<\/a><\/h2>\n

D\u00e9terminer, en le d\u00e9montrant, les variations de la fonction $f$ d\u00e9finie sur $\\mathbb R$ par $f (x) = -3(x -1)^2 +1$<\/p>\n

Exercice 4 : Correction en vid\u00e9o<\/a>
\n<\/strong><\/h2>\n

Soit $f$ le polyn\u00f4me d\u00e9fini sur $\\mathbb{R} $ par $f(x)=3x^2+6x-9$.
\nD\u00e9terminer la forme factoris\u00e9e de $f$ si elle existe.<\/p>\n

Exercice 5 : <\/strong>Correction en vid\u00e9o<\/a><\/strong><\/h2>\n

R\u00e9soudre dans $\\mathbb{R} $ : $3 x^{2}-11 x+14<0$<\/p>\n

Exercice 6 : <\/strong>Correction en vid\u00e9o<\/a><\/strong><\/h2>\n

R\u00e9soudre dans $\\mathbb{R} $ , l’in\u00e9quation :$$ \\dfrac{3x^2-4x+1}{2-3x} < 0$$<\/p>\n

Exercice 7 : <\/strong>Correction en vid\u00e9o<\/a><\/strong><\/h2>\n

Pour chacun de ces polyn\u00f4mes, d\u00e9terminer en justifiant par les r\u00e9sultats de cours, son tableau de variations :
\n$\\bullet$ $f(x)=3x^2-2x+4$
\n$\\bullet$ $g(x)=-2(x+1)^2-2$<\/p>\n

Exercice 8 : Correction en vid\u00e9o<\/a>
\n<\/strong><\/h2>\n

On donne ci-dessous, la repr\u00e9sentation graphique d’une fonction polyn\u00f4me du second degr\u00e9.\\\\
\nLes param\u00e8tres $a$, $\\alpha$ et $\\beta$, et le coefficient $\\Delta$ sont ceux utilis\u00e9s dans le cours.\\\\
\nEn justifiant par des \u00e9l\u00e9ments graphiques :<\/p>\n

    \n
  1. Que peut-on dire de $a$ ?<\/li>\n
  2. Que peut-on dire de $\\Delta$ ?<\/li>\n
  3. Que peut-on dire de $\\alpha$ et $\\beta$ ?<\/li>\n<\/ol>\n

    \"\"<\/p>\n

     <\/p>\n","protected":false},"excerpt":{"rendered":"

    Exercice 1 :\u00a0Correction en vid\u00e9o Soit $f$ la fonction d\u00e9finie sur $\\mathbb R$ par $f (x) = 2(x +3)^2 -2$ 1. D\u00e9terminer la forme d\u00e9velopp\u00e9e de $f$ 2. R\u00e9soudre, sans utiliser le discriminant : a. $f (x) = 6$ b.$f … Continuer la lecture →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-8524","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/8524","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8524"}],"version-history":[{"count":6,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/8524\/revisions"}],"predecessor-version":[{"id":8531,"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=\/wp\/v2\/pages\/8524\/revisions\/8531"}],"wp:attachment":[{"href":"https:\/\/mathsguyon.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8524"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}