Question

二次函数如果一条抛物线y=ax^2+bx+c与X轴有2个交点,那么以该抛物线的顶点和这两个交点为顶点的三角形称为这条抛物

Answer 1

y = -x² + bx = x(b - x)

与X轴有2个交点:O(0,0),A(b,0)

对称轴:x = (0 + b)/2 = b/2

x = b/2,y = -b²/4 + b*b/2 = b²/4

顶点B(b/2,b²/4)

OB的斜率m = (b²/4)/(b/2) = b/2

AB的斜率n = (b²/4 - 0)/(b/2 - b) = -b/2

mn = -1 = -b²/4

b = ±2