Quiz — exercice_corrig_forme_cadratique.pdf

Question 1 sur 10 20:00

[{"id":44175,"question":"Quelle est la forme canonique d'une fonction quadratique f(x) = ax² + bx + c ?","option_a":"f(x) = a(x - h)² + k","option_b":"f(x) = a(x + h)² + k","option_c":"f(x) = a(x - h)² - k","option_d":"f(x) = a(x + h)² - k","option_e":"","option_f":"","bonne_reponse":"a","explication":"La forme canonique d'une fonction quadratique est f(x) = a(x - h)² + k, où (h, k) sont les coordonnées du sommet de la parabole.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"f(x) = a(x - h)² + k\", \"b\": \"f(x) = a(x + h)² + k\", \"c\": \"f(x) ","_debug_options_count":4},{"id":44176,"question":"Le discriminant d'une équation quadratique est toujours positif.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le discriminant peut être positif, nul ou négatif. Il détermine le nombre de solutions réelles de l'équation.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":44177,"question":"Quelle méthode est la plus adaptée pour résoudre x² - 5x + 6 = 0 ?","option_a":"Utiliser le discriminant","option_b":"Factoriser","option_c":"Compléter le carré","option_d":"Utiliser la formule quadratique","option_e":"","option_f":"","bonne_reponse":"b","explication":"Cette équation est factorisable : (x - 2)(x - 3) = 0. Les solutions sont x = 2 et x = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Utiliser le discriminant\", \"b\": \"Factoriser\", \"c\": \"Compléter le","_debug_options_count":4},{"id":44178,"question":"Si le discriminant d'une équation quadratique est nul, combien de solutions réelles possède-t-elle ?","option_a":"Aucune","option_b":"Une solution double","option_c":"Deux solutions distinctes","option_d":"Infinité de solutions","option_e":"","option_f":"","bonne_reponse":"b","explication":"Un discriminant nul signifie que l'équation admet une solution double (racine double).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Aucune\", \"b\": \"Une solution double\", \"c\": \"Deux solutions distinc","_debug_options_count":4},{"id":44179,"question":"La parabole représentative d'une fonction quadratique f(x) = -2x² + 4x - 1 est tournée vers le bas.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le coefficient de x² est négatif (-2), donc la parabole est tournée vers le bas.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":44180,"question":"Quelle est la formule du discriminant Δ pour une équation quadratique ax² + bx + c = 0 ?","option_a":"Δ = b² - 4ac","option_b":"Δ = b² + 4ac","option_c":"Δ = 4ac - b²","option_d":"Δ = a² - 4bc","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le discriminant est donné par la formule Δ = b² - 4ac.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Δ = b² - 4ac\", \"b\": \"Δ = b² + 4ac\", \"c\": \"Δ = 4ac - b²\", \"d","_debug_options_count":4},{"id":44181,"question":"Pour résoudre une équation quadratique incomplète (sans terme constant), quelle méthode est la plus efficace ?","option_a":"Factorisation","option_b":"Discriminant","option_c":"Complétion de carré","option_d":"Formule quadratique","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une équation incomplète (c = 0), on peut factoriser directement : x(ax + b) = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Factorisation\", \"b\": \"Discriminant\", \"c\": \"Complétion de carré\"","_debug_options_count":4},{"id":44182,"question":"Le sommet de la parabole f(x) = 3x² - 6x + 2 a pour abscisse x = 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'abscisse du sommet est donnée par x = -b\/(2a) = 6\/6 = 1. L'affirmation est donc vraie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":44183,"question":"Quelle est la somme des racines d'une équation quadratique ax² + bx + c = 0 ?","option_a":"-b\/a","option_b":"b\/a","option_c":"-c\/a","option_d":"c\/a","option_e":"","option_f":"","bonne_reponse":"a","explication":"La somme des racines est donnée par -b\/a (relation de Viète).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"-b\/a\", \"b\": \"b\/a\", \"c\": \"-c\/a\", \"d\": \"c\/a\"}}","_debug_options_count":4},{"id":44184,"question":"Si a \u003E 0 dans une fonction quadratique f(x) = ax² + bx + c, la parabole admet un minimum.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Si a \u003E 0, la parabole est tournée vers le haut et admet un minimum. Si a \u003C 0, elle admet un maximum.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]