Question

如图,已知抛物线经过点A(-1,0),B(3,0),C(0,3)三点 求抛物线的解析式

Answer 1

(1)

设抛物线解析式为：y = ax + bx + c

a - b + c = 0

9a + 3b + c = 0

c = 3

a = -1 , b = 2 , c = 3

y = -x + 2x + 3

(2)

BC : x/3 + y/3 = 1 → x + y - 3 = 0

M (m , -m + 3)

N (m , -m + 2m + 3)

|MN| = 3m - m

(3)

S△BNC = 1.5 (3m - m) = -1.5(m - 1.5) + 3.375

m = 1.5 , max(S△BNC) = 3.375