(1) 对称轴为直线x=2,y = a(x - 2)² + d
x = 1,y = a + d = 0
x = 0,y = 4a + d = -3
a = -1,d = 1
y = -(x - 2)² + 1 = -xy = -x² + 4x - 3 = -(x - 1)(x - 3)
A(1,0),B(3,0)
(2)
①△PBC面积与△ABC面积相等时,AB为共同的底,只须高相同,即P,C纵坐标相等
-x² + 4x - 3 = -3
x = 4 (舍去0)
②BC为角ACP的平分线
AC的解析式:x - y/3 = 1,3x - y - 3 = 0
设CP斜率为k,解析式y = kx - 3,kx - y - 3= 0
B与二者距离相等:
|9 - 0 - 3|/√(9 + 1) = |3k - 0 - 3|/√(k² + 1)
3k² - 10k + 3 = 0
(3k - 1)(k - 3) = 0
k = 1/3 (舍去k = 3,此时CP与AC重合)
直线CP的解析式:y = x/3 - 3