(1) x² = 8x + 12 = 0(x-2)(x-6) = 0x = 2或x = 6A(2, 0), B(6, 0)(2)过A、B的抛物线可表示为y = a(x - 2)(x - 6)取x = 0, -3 = 12aa = -1/4y = -(x - 2)(x - 6)/4(3)对称轴： x = (6+2)/2 = 4此时y = -(4 - 2)(4 - 6)/4 = 1E(4, 1)题中有遗漏,D来历不明,估计是C关于对称轴的对称点,以下按此做.CE = √[(4-0)² + (1+3)²] = 4√2①当△CEM是等膘三角形时(i) CE = CM且M在C上方M(0, 4√2 - 3)(ii) CE = CM且M在C下方M(0, -4√2 - 3)(iii) CM = EM设M(0, m)CM = |m +3|EM = √[(4-0)² + (m - 1)²] = √[16 + (m - 1)²]√[16 + (m - 1)²] = |m +3|两边平方,解得m = 1M(0, 1)(iv) CE = EM设M(0, m)CE = 4√2EM = √[(4-0)² + (m - 1)²] = √[16 + (m - 1)²]√[16 + (m - 1)²] = 4√2两边平方,解得m = 5或m = -3(此为C,舍去)M(0, 5)
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