1.A) W=(0,0) 3) f(x) = ax² + bx + c f(-6) = -1 f(0) = -1 p=- 6+0/2 = -3 q = -2 f(x) = a(x-p)² + q f(x) = a(x+3)² - 2=a(x² + 6x + 9) - 2 = ax² + 6ax + 9a - 2 f(0) = -1 -1 = 9a - 2 a = 1/9 Odp. f(x) = 1/9x² + 2/3x -1 4) y = ½x² + 5x - 1 p = -5/1 = -5 q = f(p) = = f(-5) = ½ * 25 - 25 - 1 = 12½ - 26 = -13½ postać kanoniczna: y = ½(x +5)² - 13½ 8) y = x² + 5x + 2 y = - x - 6 x² + 5x + 2 = -x -6 x² + 6x + 8 = 0 Δ = 36 -32 = 4 √Δ = 2 X1 = -6-2/2 = -4 X2 = -6+2/2 = -2 x=-4 lub x=-2 y=-2 y=-4 Odp. A(-4,-2), B(-2,-4) 11) a) f(0) = - 0,35 * 0 + 2 * 0 + 0,6 = 0,6m c) q = ? Δ= 4 - 4*(-0,35)*0,6=4+0,84=4,84 q = -4,84/4*(-0,35) = 3,457143 = 3 i 16/35m
