抛物线y1=-ax^2-ax+1经过点(-1/2,9/8),且与抛物线y2=ax^2-ax-1相交于A,B两点抛物线y1=-ax^2-ax+1经过点(-1/2,9/8),且与抛物线y2=ax^2-ax-1相交于A,B两点.设A,B两点的横坐标分别记为xA,xB,若在x轴上有一动点Q(
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![抛物线y1=-ax^2-ax+1经过点(-1/2,9/8),且与抛物线y2=ax^2-ax-1相交于A,B两点抛物线y1=-ax^2-ax+1经过点(-1/2,9/8),且与抛物线y2=ax^2-ax-1相交于A,B两点.设A,B两点的横坐标分别记为xA,xB,若在x轴上有一动点Q(](/uploads/image/z/11534214-30-4.jpg?t=%E6%8A%9B%E7%89%A9%E7%BA%BFy1%3D-ax%5E2-ax%2B1%E7%BB%8F%E8%BF%87%E7%82%B9%28-1%2F2%2C9%2F8%29%2C%E4%B8%94%E4%B8%8E%E6%8A%9B%E7%89%A9%E7%BA%BFy2%3Dax%5E2-ax-1%E7%9B%B8%E4%BA%A4%E4%BA%8EA%2CB%E4%B8%A4%E7%82%B9%E6%8A%9B%E7%89%A9%E7%BA%BFy1%3D-ax%5E2-ax%2B1%E7%BB%8F%E8%BF%87%E7%82%B9%EF%BC%88-1%2F2%2C9%2F8%EF%BC%89%2C%E4%B8%94%E4%B8%8E%E6%8A%9B%E7%89%A9%E7%BA%BFy2%3Dax%5E2-ax-1%E7%9B%B8%E4%BA%A4%E4%BA%8EA%2CB%E4%B8%A4%E7%82%B9.%E8%AE%BEA%2CB%E4%B8%A4%E7%82%B9%E7%9A%84%E6%A8%AA%E5%9D%90%E6%A0%87%E5%88%86%E5%88%AB%E8%AE%B0%E4%B8%BAxA%2CxB%2C%E8%8B%A5%E5%9C%A8x%E8%BD%B4%E4%B8%8A%E6%9C%89%E4%B8%80%E5%8A%A8%E7%82%B9Q%EF%BC%88)
抛物线y1=-ax^2-ax+1经过点(-1/2,9/8),且与抛物线y2=ax^2-ax-1相交于A,B两点抛物线y1=-ax^2-ax+1经过点(-1/2,9/8),且与抛物线y2=ax^2-ax-1相交于A,B两点.设A,B两点的横坐标分别记为xA,xB,若在x轴上有一动点Q(
抛物线y1=-ax^2-ax+1经过点(-1/2,9/8),且与抛物线y2=ax^2-ax-1相交于A,B两点
抛物线y1=-ax^2-ax+1经过点(-1/2,9/8),且与抛物线y2=ax^2-ax-1相交于A,B两点.
设A,B两点的横坐标分别记为xA,xB,若在x轴上有一动点Q(x,0),且xA小于等于x小于等于xB,过Q作一条垂直于x轴的直线,与两条抛物线分别交于C,D两点,试问当x为何值时,线段CD有最大值,其最大值为多少?
抛物线y1=-ax^2-ax+1经过点(-1/2,9/8),且与抛物线y2=ax^2-ax-1相交于A,B两点抛物线y1=-ax^2-ax+1经过点(-1/2,9/8),且与抛物线y2=ax^2-ax-1相交于A,B两点.设A,B两点的横坐标分别记为xA,xB,若在x轴上有一动点Q(
由题意9/8=-a/4+a/2+1
a/4=1/8 a=2
y1=-2x^2-2x+1
y2=2x^2-2x-1
两方程联立得
-2x^2-2x+1=2x^2-2x-1
4x^2=2 x=正负√2/2
故xA=-√2/2 xB=√2/2
而CD=|y1-y2|=|-4x^2+2|
又-√2/2=
将点(-1/2,9/8)代入抛物线y1=-ax^2-ax+1
9/8=-(-1/2)^2 a-(-1/2)a+1=-(1/4)a+(1/2)a+1 ,a=1/2
y1=-(1/2)x^2-(1/2)x+1 , y2=(1/2)x^2-(1/2)x-1
两式联立,得:x=±√2 ,即:-√2≤x≤√2
过Q(x,0)作一条垂直于x轴的直线CD
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将点(-1/2,9/8)代入抛物线y1=-ax^2-ax+1
9/8=-(-1/2)^2 a-(-1/2)a+1=-(1/4)a+(1/2)a+1 ,a=1/2
y1=-(1/2)x^2-(1/2)x+1 , y2=(1/2)x^2-(1/2)x-1
两式联立,得:x=±√2 ,即:-√2≤x≤√2
过Q(x,0)作一条垂直于x轴的直线CD
CD=√(x-x)^2+(y2-y1)^2=√(x^2-2)^2=│x^2-2│
∵-√2≤x≤√2
∴当x=0时,线段CD有最大值,最大值为2
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