91.(08新疆自治区24题)(10分)某工厂要赶制一批抗震救灾用的大型活动板房.如图,板房一面的形状是由矩形和抛物线的一部分组成,矩形长为12m,抛物线拱高为5.6m.

(1)在如图所示的平面直角坐标系中,求抛物线的表达式.

(2)现需在抛物线AOB的区域内安装几扇窗户,窗户的底边在AB上,每扇窗户宽1.5m,高1.6m,相邻窗户之间的间距均为0.8m,左右两边窗户的窗角所在的点到抛物线的水平距离至少为0.8m.请计算最多可安装几扇这样的窗户?

(08新疆自治区24题解析)24.(10分)解:(1)设抛物线的表达式为  1分

点在抛物线的图象上.

∴

······························································ 3分

∴抛物线的表达式为············································································· 4分

(2)设窗户上边所在直线交抛物线于C、D两点,D点坐标为(k,t)

已知窗户高1.6m,∴··························································· 5分

(舍去)············································································ 6分

∴(m)·············································································· 7分

又设最多可安装n扇窗户

∴····················································································· 9分

.

答:最多可安装4扇窗户.···················································································· 10分

(本题不要求学生画出4个表示窗户的小矩形)

89.(08四川巴中30题)(12分)30.已知:如图14,抛物线与轴交于点,点,与直线相交于点,点,直线与轴交于点.

(1)写出直线的解析式.

(2)求的面积.

(3)若点在线段上以每秒1个单位长度的速度从向运动(不与重合),同时,点在射线上以每秒2个单位长度的速度从向运动.设运动时间为秒,请写出的面积与的函数关系式,并求出点运动多少时间时,的面积最大,最大面积是多少?

(08四川巴中30题解析)解:(1)在中,令

,

,··············································· 1分

又点在上

的解析式为·············································································· 2分

(2)由,得  ···················································· 4分

,

,······························································································· 5分

························································································· 6分

(3)过点作于点

······························································································· 7分

·········································································································· 8分

由直线可得:

在中,,,则

,······················································································· 9分

···················································································· 10分

····························································································· 11分

此抛物线开口向下,当时,

当点运动2秒时,的面积达到最大,最大为.···························· 12分

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