y = (x - 1)(x - 3)
A(1,0),B(3,0),C(0,3)
AC = √10,MN = 2√10
向左平移后p后的抛物线:y = (x - 1+ p)(x - 3+p)
AC的解析式:x + y/3 = 1,y = -3(x - 1)
联立得:x² + (2p - 1)x + p² - 4p = 0
x₁ + x₂ = 1 - 2p
x₁x₂ = p² - 4p
MN² = 40 = (x₁ - x₂)²+ (y₁ - y₂)² = (x₁ - x₂)²+ (-3x₁ +3 + 3x₂- 3)² = 10(x₁ - x₂)²
(x₁ - x₂)² = 4 = (x₁ + x₂)² - 4x₁x₂ = 4p² - 4p + 1 - 4(p² - 4p) = 12p + 1
p = 1/4
向左平移后1/4后的抛物线:y = (x - 1+ 1/4)(x - 3+1/4) = (x - 3/4)(x - 11/4)为什么要用交点式平移？