已知二次函数y=ax2 bx c的图像与x轴交于A(-2,0),B(4,0)两点,与y轴交于点C(
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(1)
y=ax^2+ bx+ c
C(0,4) => c= 4
y=ax^2+ bx+ 4
A(-2,0)
4a-2b+4 =0
2a-b = -2 (1)
B(4,0)
16a+4b+4 =0
4a+b = -1 (2)
(1)+(2)
6a=-3
a=-1/2
from (2)
4a+b = -1
-2+b = -1
b=1
y = -(1/2)x^2 +x +4
(2)
y = -(1/2)x^2 +x +4
= -(1/2)(x-1)^2 + 9/2
顶点坐标 =( 1, 9/2)
y=ax^2+ bx+ c
C(0,4) => c= 4
y=ax^2+ bx+ 4
A(-2,0)
4a-2b+4 =0
2a-b = -2 (1)
B(4,0)
16a+4b+4 =0
4a+b = -1 (2)
(1)+(2)
6a=-3
a=-1/2
from (2)
4a+b = -1
-2+b = -1
b=1
y = -(1/2)x^2 +x +4
(2)
y = -(1/2)x^2 +x +4
= -(1/2)(x-1)^2 + 9/2
顶点坐标 =( 1, 9/2)
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