Question

抛物线y=a乘以x的平方+bx+c的对称轴是x=-1,与x轴两交点间的距离为4,且经过点(0,-6),则该抛物线的表达式

Answer 1

设X,X'是抛物线与X轴的交点

则X+X'=-b/a

XX'=C/a

/X-X'/./X-X'/=XX+X'X'-2XX'=XX+X'X'+2XX'-4XX'=(X+X')(X+X')-4XX'

=(b/a)(b/a)-4c/a=16

-b/2a=-1

b/a=2 b=2a 1

代入/?中得c/a=-3 c=-3a 2

(0,-6)在抛物线上则-6=c 3

a=2 b=4

y=2aa+4b-6