1.y=ax^2+bx+c的顶点的横坐标为-b/2a,由图可知,-b/(2a) = 2
b = -4a (1)
y=ax^2+bx+c过(1,0),(2,2):
a + b + c = 0 (2)
4a + 2b + c = 2 (3)
解(1)-(3):a = -2,b = 8,c = -6
y = -2x^2 +8x -6 = -2(x-1)(x-3)
ax^2+bx+c=0的解集为x=1或x=3
2.由图可知,ax^2+bx+c>0的解集为1 < x < 3
3.y 随 x 的增大而减小的自变量x的取值范围:x > 2
4.ax^2+bx+c=k
-2x^2 +8x -6 = k
-2x^2 +8x -6 - k = 0
8^2 -4(-2)(-6-k) = 64 -8(6+k) > 0
8 - (6+k) > 0
2 -k > 0
k < 2