试题分析:(1)∵函数的值域为[0,+∞),
∴Δ=16a
2-4(2a+6)=0-----3分
⇒2a
2-a-3=0⇒a=-1或a=
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824001429025389.png)
.-----------------7分
(2)函数
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824001428916913.png)
在
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824001429103613.png)
上是单调递增的,
要使
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824001428932463.png)
在
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824001428994515.png)
上是增函数,只需
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824001429150456.png)
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824001429041389.png)
所以实数
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824001429010283.png)
的取值范围为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824001429259551.png)
点评:我们研究二次函数的单调性和最值时一定要考虑它的开口方向。①最大(小)值:当a>0时,函数图象开口向上,y有最小值,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824001429291848.png)
,无最大值;当a<0时,函数图象开口向下,y有最大值,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824001429306888.png)
,无最小值。②当a>0时,函数在区间
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824001429400853.png)
上是减函数,在
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824001429447808.png)
上是增函数;当a<0时,函数在区间上
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824001429447808.png)
是减函数,在
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824001429400853.png)
上是增函数。