Maîtrisez les paraboles : fonctions quadratiques et équations du second degré

Question 1 sur 10 10:00

[{"id":19118,"question":"Quelle est la forme canonique d'une fonction quadratique f(x) = ax² + bx + c ?","option_a":"f(x) = a(x - α)² + β","option_b":"f(x) = a(x + α)² + β","option_c":"f(x) = a(x - β)² + α","option_d":"f(x) = a(x + β)² + α","option_e":"","option_f":"","bonne_reponse":"A","explication":"La forme canonique d'une fonction quadratique est f(x) = a(x - α)² + β, où (α, β) sont les coordonnées du sommet de la parabole.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19119,"question":"Si une équation du second degré a un discriminant strictement négatif, alors elle admet :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Un discriminant négatif signifie qu'il n'y a pas de solutions réelles (les solutions sont complexes).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19120,"question":"Pour la fonction f(x) = 2x² - 8x + 6, quelle est la somme des racines ?","option_a":"4","option_b":"-4","option_c":"3","option_d":"-3","option_e":"","option_f":"","bonne_reponse":"A","explication":"La somme des racines d'une équation ax² + bx + c = 0 est -b\/a. Ici, -(-8)\/2 = 4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19121,"question":"Le sommet de la parabole d'équation y = -x² + 4x - 3 a pour coordonnées :","option_a":"(2, 1)","option_b":"(1, 0)","option_c":"(0, -3)","option_d":"(-2, -11)","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'abscisse du sommet est x = -b\/(2a) = -4\/(2*(-1)) = 2. L'ordonnée est f(2) = -(2)² + 4*2 - 3 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19122,"question":"Si a \u003E 0 dans f(x) = ax² + bx + c, alors la parabole est tournée vers le bas.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","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":19123,"question":"Quelle est la formule du discriminant Δ pour une équation du second degré 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},{"id":19124,"question":"Pour la fonction f(x) = x² - 6x + 8, le produit des racines est égal à :","option_a":"8","option_b":"-8","option_c":"6","option_d":"-6","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le produit des racines d'une équation ax² + bx + c = 0 est c\/a. Ici, 8\/1 = 8.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19125,"question":"L'axe de symétrie d'une parabole est toujours vertical.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'axe de symétrie d'une parabole est toujours une droite verticale d'équation x = -b\/(2a).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19126,"question":"Si une parabole coupe l'axe des abscisses en deux points distincts, alors son discriminant est :","option_a":"Positif","option_b":"Nul","option_c":"Négatif","option_d":"Indéterminé","option_e":"","option_f":"","bonne_reponse":"A","explication":"Si la parabole coupe l'axe des abscisses en deux points distincts, cela signifie qu'il y a deux solutions réelles distinctes, donc Δ \u003E 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":19127,"question":"Quelle est la valeur du discriminant pour l'équation 3x² - 5x + 2 = 0 ?","option_a":"1","option_b":"-1","option_c":"17","option_d":"25","option_e":"","option_f":"","bonne_reponse":"C","explication":"Δ = b² - 4ac = (-5)² - 4*3*2 = 25 - 24 = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]