La parabole qui represente graphiquement la fonction polynome f du second degré f est telle que f(2)=f(-4)=0 et a pour maximum 5 determiner lexpression f(x)

f(x) = a x² + b x + c

f(2) = 4a + 2b + c = 0
f(-4) = 16a - 4b + c = 0
f(-1) = a - b + c = 5

cela donne : 4a + 2b + c = 0
                    4a - b + 0,25c = 0
                    4a - 4b + 4c = 2o

par soustraction des équations repassées en gras : 6b - 3c = -2o
                                                                                    2b - c = -2o/3
                                                                                         2b = c - 2o/3
le système devient : 4a + 2c - 2o/3 = 0
                                 4a - 0,25c + 2o/6 = 0
                                 4a + 2c + 4o/3 = 6o/3

par soustraction des équations repassées en gras :
                                2,25 c - 2o/3 - 2o/6 = 0
                                                    2,25 c = 2o/3 + 1o/3
                                                    2,25 c = 1o
                                                            c = 4o/9
donc 2 b = c - 2o/3 = 4o/9 - 6o/9 = - 2o/9 d' où b = - 1o/9

donc a = 5 + b - c = 45/9 - 1o/9 - 4o/9 = - 5/9

conclusion : f(x) = (-5/9) x² - (1o/9) x + (4o/9)