二次函数问题,急啊高手帮忙!山东

1个回答

  • (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)