f(x) = - x^2 + b x + c a) f(3) = 18 czyli f(3) = -(3)^2 + b*3 + c = - 9 + 3 b + c = 18 f(-2) = - 25 czyli f( -2) = - (-2)^2 + b*(-2) + c = - 4 - 2b + c = - 25 Mamy układ równań: -9 + 3b + c = 18 -4 - 2b + c = - 25 -------------------------- odejmujemy stronami te równania -9 + 3b + c - ( -4 - 2b+ c) = 18 - (-25) -5 + 5b = 43 5b = 43 + 5 = 48 b = 9,6 ===== - 4 - 2*9,6 + c = - 25 - 4 - 19,2 + c = - 25 c = -25 + 23,2 c = -1,8 ======= Odp. f(x) = - x^2 + 9,6 x - 1,8 =========================== b) f(x) = - x^2 + b x + c f(1) = 1 zatem f(1) = - 1^2 + b*1 + c = - 1 + b + c = 1 f(-5) = 37 zatem f( -5) = - (-5)^2 + b*(-5) + c = - 25 - 5 b + c = 37 Mamy układ równań: -1 + b + c = 1 -25 - 5b + c = 37 ------------------------ b + c = 2 -5b + c = 62 ----------------- odejmujemy stronami b + c - ( - 5b + c) = 2 - 62 6 b = - 60 / : 6 b = - 10 =========== - 10 + c = 2 c = 2 - ( - 10) = 12 ============== Odp. f(x) = - x^2 - 10 x + 12 ===========================
