如图,直线L:y=1/4x+b与y轴的交点M(0,3),一组抛物线的顶点坐标分别是B1(1,y1),b2(2,y2),(b3,y3).(Bn,Yn)(n为正整数),他们依次是直线上的点,这组抛物线与X轴正半轴的交点分别是A1(X1,0)A2
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![如图,直线L:y=1/4x+b与y轴的交点M(0,3),一组抛物线的顶点坐标分别是B1(1,y1),b2(2,y2),(b3,y3).(Bn,Yn)(n为正整数),他们依次是直线上的点,这组抛物线与X轴正半轴的交点分别是A1(X1,0)A2](/uploads/image/z/9940333-13-3.jpg?t=%E5%A6%82%E5%9B%BE%2C%E7%9B%B4%E7%BA%BFL%EF%BC%9Ay%3D1%2F4x%2Bb%E4%B8%8Ey%E8%BD%B4%E7%9A%84%E4%BA%A4%E7%82%B9M%280%2C3%29%2C%E4%B8%80%E7%BB%84%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E9%A1%B6%E7%82%B9%E5%9D%90%E6%A0%87%E5%88%86%E5%88%AB%E6%98%AFB1%EF%BC%881%2Cy1%EF%BC%89%2Cb2%EF%BC%882%2Cy2%EF%BC%89%2C%EF%BC%88b3%2Cy3%EF%BC%89.%EF%BC%88Bn%2CYn%EF%BC%89%EF%BC%88n%E4%B8%BA%E6%AD%A3%E6%95%B4%E6%95%B0%EF%BC%89%2C%E4%BB%96%E4%BB%AC%E4%BE%9D%E6%AC%A1%E6%98%AF%E7%9B%B4%E7%BA%BF%E4%B8%8A%E7%9A%84%E7%82%B9%2C%E8%BF%99%E7%BB%84%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%B8%8EX%E8%BD%B4%E6%AD%A3%E5%8D%8A%E8%BD%B4%E7%9A%84%E4%BA%A4%E7%82%B9%E5%88%86%E5%88%AB%E6%98%AFA1%EF%BC%88X1%2C0%EF%BC%89A2)
如图,直线L:y=1/4x+b与y轴的交点M(0,3),一组抛物线的顶点坐标分别是B1(1,y1),b2(2,y2),(b3,y3).(Bn,Yn)(n为正整数),他们依次是直线上的点,这组抛物线与X轴正半轴的交点分别是A1(X1,0)A2
如图,直线L:y=1/4x+b与y轴的交点M(0,3),一组抛物线的顶点坐标分别是B1(1,y1),b2(2,y2),(b3,y3).(Bn,Yn)(n为正整数),他们依次是直线上的点,这组抛物线与X轴正半轴的交点分别是A1(X1,0)A2(X2,0)A3(X3,0).An+1(Xn+1,0)(n为正整数),设x1=a(0
如图,直线L:y=1/4x+b与y轴的交点M(0,3),一组抛物线的顶点坐标分别是B1(1,y1),b2(2,y2),(b3,y3).(Bn,Yn)(n为正整数),他们依次是直线上的点,这组抛物线与X轴正半轴的交点分别是A1(X1,0)A2
(1)易求出b=3,y1=13/4,设所求抛物线方程为y=c(x-1)^2+13/4,它经过点A1,所以c(a-1)^2+13/4=0,得c=-13/【4(a-1)^2】,抛物线方程为y=-13/【4(a-1)^2】*(x-1)^2+13/4
(2)对于从左至右第n条抛物线,其顶点为(n,n/4+3).第n条抛物线与x轴的为An,An+1,则An+A(n+1)=2n,(两点关于对称轴对称),故有A(n+2)+A(n)=2(n+1).两式相减得:A(n+2)-An=2,而第n条与第n+1条抛物线与x轴两交点距离之和为【A(n+1)-An】+【A(n+2)-A(n+1)】=A(n+2)-An=2,所以相邻两条抛物线与x轴两交点距离之和始终为2