题干

如图,在平面直角坐标系中,点0为坐标原点,抛物线y=ax2+bx+4与y轴交于点A,与x轴交于点B、C(点B在点C左侧),且OA=OC=4OB.
(1)求a,b的值;
(2)连接AB、AC,点P是抛物线上第一象限内一动点,且点P位于对称轴右侧,
过点P作PD⊥AC于点E,分别交x、y轴于点D、H,过点P作PG∥AB交AC于点F,交x轴于点G,设P(x,y),线段DG的长为d,求d与x之间的函数关系(不要求写出自变量x的取值范围);
(3)在(2)的条件下,当
S
P
E
F
S
P
D
F
=
3
8
时,连接AP并延长至点M,连接HM交AC于点S,点R是抛物线上一动点,当△ARS为等腰直角三角形时.求点R的坐标和线段AM的长.
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答案(点此获取答案解析)

解:(1)y=ax2+bx+4,当x=0时,y=4,

∴A(0,4)

∵OC=OA=4OB,

∴OC=4,OB=1,

∴C(4,0),B(﹣1,0)

将C(4,0),B(﹣1,0)代入抛物线y=ax2+bx+4

得:

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