如图已知一交函数y=-2x+6的图像与x轴交于点A,与y轴交于点C,二次函数y=ax²+bx+c（a≠0）的图

(1) A(3,0),C(0,6)
代入y=ax²+bx+c c = 6 b = -3a -2
y = ax² -(3a+2)x + 6
设B(p,0),3(A的横坐标),p为ax² -(3a+2)x + 6 = 0的解
y = ax² -(3a+2)x + 6 = a(x-p)(x-3) = ax² -(p+3)ax + 3ap
3a+2 = (p+3)a,ap = 2 S△ABC = 4S△BOC
△ABC 和△BOC高均|OC|,故|AB| = 4|OB |AB| = 3 - p
|OB| = 0-p = -p p = -1 a = 2/p = -2 ,b= -3a -2 = 4
得：抛物线的解析式:y = -2x² + 4x + 6
(2)以OA的长为直径作圆M,M(3/2,0),圆半径 r = 3/2
M与y=-2x+6 (2x + y - 6 = 0)的距离为d = |(3/2)*2 + 0 - 6|/√(2²+1²) = 3/√5 = 3√5/5 < 3/2
圆M与直线AC相交.