Quiz : Maîtrisez les fonctions et équations du second degré !

Question 1 sur 10 10:00

[{"id":49441,"question":"Quelle est la forme générale d'une fonction du second degré ?","option_a":"f(x) = ax + b","option_b":"f(x) = ax² + bx + c","option_c":"f(x) = a\/x","option_d":"f(x) = √x","option_e":"","option_f":"","bonne_reponse":"B","explication":"La forme générale d'une fonction du second degré est f(x) = ax² + bx + c, où a, b et c sont des réels et a ≠ 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49442,"question":"Le discriminant d'une équation du second degré 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 selon les valeurs de a, b et c.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49443,"question":"Si Δ \u003E 0, l'équation du second degré admet :","option_a":"Une seule solution","option_b":"Deux solutions distinctes","option_c":"Aucune solution","option_d":"Une infinité de solutions","option_e":"","option_f":"","bonne_reponse":"B","explication":"Lorsque Δ \u003E 0, l'équation admet deux solutions distinctes données par x = (-b ± √Δ) \/ (2a).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49444,"question":"La parabole d'une fonction du second degré f(x) = ax² + bx + c est tournée vers le haut si :","option_a":"a \u003E 0","option_b":"a \u003C 0","option_c":"b \u003E 0","option_d":"c \u003E 0","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si a \u003E 0, la parabole est tournée vers le haut. Si a \u003C 0, elle est tournée vers le bas.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49445,"question":"L'équation x² - 4x + 4 = 0 admet :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Cette équation admet une solution double x = 2, car Δ = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49446,"question":"Quelle est la formule de la forme canonique d'un polynôme du second degré ?","option_a":"f(x) = a(x - α)² + β","option_b":"f(x) = a(x + α)² + β","option_c":"f(x) = a(x - α)(x - β)","option_d":"f(x) = ax² + bx + c","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique est f(x) = a(x - α)² + β, où α et β sont les coordonnées du sommet de la parabole.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49447,"question":"Si a \u003C 0 dans f(x) = ax² + bx + c, alors la fonction est :","option_a":"Croissante sur ℝ","option_b":"Décroissante sur ℝ","option_c":"Constante","option_d":"Non définie","option_e":"","option_f":"","bonne_reponse":"B","explication":"Si a \u003C 0, la fonction est décroissante sur ℝ, car la parabole est tournée vers le bas.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49448,"question":"L'inéquation x² - 5x + 6 \u003E 0 admet comme solution :","option_a":"x ∈ ]2 ; 3[","option_b":"x ∈ ]-∞ ; 2[ ∪ ]3 ; +∞[","option_c":"x ∈ ℝ","option_d":"x ∈ ∅","option_e":"","option_f":"","bonne_reponse":"B","explication":"Les racines sont x = 2 et x = 3. Le polynôme est positif à l'extérieur de l'intervalle [2 ; 3].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49449,"question":"Le sommet de la parabole f(x) = 2x² - 8x + 5 a pour abscisse :","option_a":"x = 1","option_b":"x = 2","option_c":"x = 4","option_d":"x = -2","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'abscisse du sommet est donnée par x = -b\/(2a) = 8\/4 = 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49450,"question":"Une fonction du second degré peut-elle avoir un minimum et un maximum ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Une fonction du second degré n'a qu'un seul extremum (minimum si a \u003E 0, maximum si a \u003C 0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]