(1)把A点坐标代入二次函数,得
a=-1 即y=-x2
代入y=-4,解得x=±2
B(2,-4)
设AB与y轴交于C,则C为(0,-4)
S△AOB=1/2 |AB|×|OC|=1/2|xA-xB||yC|=1/2|-2-2||-4|=(1/2)×4×4=8
(2)设:P点坐标为(X0,Y0),P做垂线交AB于D,则D(X0,-4)
Y0=-X02
∵2×S△PAB=△AOB
∴2×(1/2)×|PD|×|AB|=|-4-Y0||xA-xB|=8
∴|-4-Y0|=-2
解得Y0=-6或-2
将Y0=-6或-2分别代入方程y=-x2
得P(√6,-6)或(-√6,-6)或(√2,-2)或(-√2,-2)
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