Question

已知抛物线y=x²+bx+c经过A（-1,0）,B（3,0）两点

Answer 1

(1)
A(3,
0),
B(0,
3)
抛物线过A,
C(均在x轴上):
y
=
a(x
-
3)(x
-
1)
x
=
0,
y
=
3a
=
3,
a
=
1
y
=
(x
-
3)(x
-
1)
=
x2
-
4x
+
3
(2)
OA
=
OB
=
3,
△ABO是等腰直角三角形
△ABO与△ADP相似
DP⊥AB,
DP
=
DA
AB的斜率=
-1,
DP的斜率
=
1,
DP的解析式:
y
=
1(x
+
1)
=
x
+
1
与y
=
-x
+
3联立,
P(1,
2)
(3)
E(e,
e2
-
4e
+
3),
1<
e
<
3
△ADE的面积S1
=
(1/2)(3
+
1)(-e2
+
4e
-
3)
=
2(-e2
+
4e
-
3)
四边形APCE的面积S2
=
△ACP的面积
+
△ACE的面积
=
(1/2)(3
-
1)*2
+
(1/2)*2*(-e2
+
4e
-
3)
=
2
-e2
+
4e
-
3
S1
=
S2
2(-e2
+
4e
-
3)
=
2
-e2
+
4e
-
3
-e2
+
4e
-
3
=
2
e2
-
4e
+
5=
0
△
=
16
-
20
=
-4
<
0
E不存在