16) y=x²/2-3x+4
=1/2(x²-6+8)
=1/2(x²-2·3+3²-1)
=1/2(x²-2·3+3²)-1/2
=1/2(x-3)²-1/2
所以其顶点为(3,-1/2)
对称轴 x=3
y=1/2(x-3)²-1/2<0
1/2(x-3)²<1/2
(x-3)²<1
-1
2
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17)将(3,0)、(2,-3)代入y=x²+bx+c得:
0=3²+3b+c
-3=2²+2b+c
联立求解得:b=-2,c=-3
所以抛物线为y=x²-2x-3
其顶点P为[-b/(2a),(4ac-b²)/(4a)]
即P(1,-4)
与纵轴交点Q(0,-3)
OQ=0-(-3)=3
OQ边上的高为P到纵轴的距离1
所以S△OPQ=3×1÷2=1/2