(1)C關(guān)于直線OB對(duì)稱,AB=BC
∵ OB⊥AB,OB=√3,OA=2 ∴ AB=1=OA/2
∴ ∠AOB=30°,∠OAB=60°,又AC=2=OA
∴ △OAC是等邊三角形
∵ OD=2OA=4,A是OD的中點(diǎn),AD=2
作PE⊥OA于E,則OE=OP/2=(2-X)/2
PE=OP*√3/2,DE=4-OE=4-1+X/2=3+X/2
∵ Rt△DPE∽R(shí)t△DAM,則
AM:PE=AD:PD,AM=PE*AD/PD
Y=0.5*AM*PD=0.5*PE*AD=(2-X)√3/2=√3-X√3/2
若二次函數(shù)Y=-2X^2-(7K-3√3)X+√3K的圖像關(guān)于Y軸對(duì)稱,即:K=3√3/7
當(dāng)X=1/2時(shí),PC=1/2,OP=3/2,OE=3/4,PE=3√3/4,DE=4-OE=4-3/4=13/4,PD^2=PE^2+DE^2
PD^2=(169+27)/16=196/16,PD=7/2,AM=PE*AD/PD,K=7AM/2PD=7PE*AD/2PD^2=7PE/PD^2
=(7*3√3/4)*(16/196)=3√3/7,將7K=3√3代入二次函數(shù)得：Y=-2X^2+9/7,
即,Y-9/7=-2X^2,該二次函數(shù)關(guān)于X=0對(duì)稱,顯然也關(guān)于Y軸對(duì)稱.