已知点A(X1,Y1)、B(X2,Y2)均在抛物线Y=ax^2+2ax+4(0

问题描述:

已知点A(X1,Y1)、B(X2,Y2)均在抛物线Y=ax^2+2ax+4(0

B

B.y1依题意可知
0x1+x2=1-a
因为0所以-2故-1又因为,对称轴x=-2a/2a=-1即抛物线上x1,x2的中点在对称轴的右边,
由抛物线的图形可知y1

将X1代入抛物线,得Y1=aX1²+2aX1+4将X2代入抛物线,得Y2=aX2²+2aX2+4Y1-Y2=a(X1²-X2²)+2a(X1-X2)=a(X1-X2)(X1+X2)+2a(X1-X2)=a(X1-X2)(X1+X2+2)∵x1+x2=1-a(代换)∴Y1-Y2=a(X1-X2)(3-a)∵0...