如图已知一交函数y=-2x+6的图像与x轴交于点A,与y轴交于点C,二次函数y=ax²+bx+c(a≠0)的图像过A,C两点,并且与x轴交于另一个点B(B在负半轴上)(1)当S△ABC=4S△BOC时,求抛物线y=ax²+bx+c的
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![如图已知一交函数y=-2x+6的图像与x轴交于点A,与y轴交于点C,二次函数y=ax²+bx+c(a≠0)的图像过A,C两点,并且与x轴交于另一个点B(B在负半轴上)(1)当S△ABC=4S△BOC时,求抛物线y=ax²+bx+c的](/uploads/image/z/1671373-37-3.jpg?t=%E5%A6%82%E5%9B%BE%E5%B7%B2%E7%9F%A5%E4%B8%80%E4%BA%A4%E5%87%BD%E6%95%B0y%3D-2x%2B6%E7%9A%84%E5%9B%BE%E5%83%8F%E4%B8%8Ex%E8%BD%B4%E4%BA%A4%E4%BA%8E%E7%82%B9A%2C%E4%B8%8Ey%E8%BD%B4%E4%BA%A4%E4%BA%8E%E7%82%B9C%2C%E4%BA%8C%E6%AC%A1%E5%87%BD%E6%95%B0y%3Dax%26sup2%3B%2Bbx%2Bc%EF%BC%88a%E2%89%A00%EF%BC%89%E7%9A%84%E5%9B%BE%E5%83%8F%E8%BF%87A%2CC%E4%B8%A4%E7%82%B9%2C%E5%B9%B6%E4%B8%94%E4%B8%8Ex%E8%BD%B4%E4%BA%A4%E4%BA%8E%E5%8F%A6%E4%B8%80%E4%B8%AA%E7%82%B9B%EF%BC%88B%E5%9C%A8%E8%B4%9F%E5%8D%8A%E8%BD%B4%E4%B8%8A%EF%BC%89%EF%BC%881%EF%BC%89%E5%BD%93S%E2%96%B3ABC%3D4S%E2%96%B3BOC%E6%97%B6%2C%E6%B1%82%E6%8A%9B%E7%89%A9%E7%BA%BFy%3Dax%26sup2%3B%2Bbx%2Bc%E7%9A%84)
如图已知一交函数y=-2x+6的图像与x轴交于点A,与y轴交于点C,二次函数y=ax²+bx+c(a≠0)的图像过A,C两点,并且与x轴交于另一个点B(B在负半轴上)(1)当S△ABC=4S△BOC时,求抛物线y=ax²+bx+c的
如图已知一交函数y=-2x+6的图像与x轴交于点A,与y轴交于点C,二次函数y=ax²+bx+c(a≠0)的图像过A,C两点,并且与x轴交于另一个点B(B在负半轴上)
(1)当S△ABC=4S△BOC时,求抛物线y=ax²+bx+c的解析式和此函数顶点坐标.
(2)以OA的长为直径作圆M,试判定圆M与直线AC的位置关系,并说明理由.
如图已知一交函数y=-2x+6的图像与x轴交于点A,与y轴交于点C,二次函数y=ax²+bx+c(a≠0)的图像过A,C两点,并且与x轴交于另一个点B(B在负半轴上)(1)当S△ABC=4S△BOC时,求抛物线y=ax²+bx+c的
(1) A(3,0),C(0,6)
代入y=ax²+bx+c c = 6 b = -3a -2
y = ax² -(3a+2)x + 6
设B(p,0),3(A的横坐标),p为ax² -(3a+2)x + 6 = 0的解
y = ax² -(3a+2)x + 6 = a(x-p)(x-3) = ax² -(p+3)ax + 3ap
3a+2 = (p+3)a,ap = 2 S△ABC = 4S△BOC
△ABC 和△BOC高均|OC|,故|AB| = 4|OB |AB| = 3 - p
|OB| = 0-p = -p p = -1 a = 2/p = -2 ,b= -3a -2 = 4
得:抛物线的解析式:y = -2x² + 4x + 6
(2)以OA的长为直径作圆M,M(3/2,0),圆半径 r = 3/2
M与y=-2x+6 (2x + y - 6 = 0)的距离为d = |(3/2)*2 + 0 - 6|/√(2²+1²) = 3/√5 = 3√5/5 < 3/2
圆M与直线AC相交.
(1) A(3, 0), C(0, 6)
代入y=ax²+bx+c:
9a + 3b + c = 0
c = 6
b = -3a -2 (1)
y = ax² -(3a+2)x + 6
设B(p, 0), 3(A的横坐标), p为ax² -(3a+2)x + 6 = ...
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(1) A(3, 0), C(0, 6)
代入y=ax²+bx+c:
9a + 3b + c = 0
c = 6
b = -3a -2 (1)
y = ax² -(3a+2)x + 6
设B(p, 0), 3(A的横坐标), p为ax² -(3a+2)x + 6 = 0的解
y = ax² -(3a+2)x + 6 = a(x-p)(x-3) = ax² -(p+3)ax + 3ap
比较系数: 3a+2 = (p+3)a, ap = 2 (2)
S△ABC = 4S△BOC
△ABC 和△BOC高均|OC|, 故|AB| = 4|OB|
|AB| = 3 - p
|OB| = 0-p = -p
3-p = -4p
p = -1
结合(2): a = 2/p = -2
结合(1): b= -3a -2 = 4
抛物线的解析式: y = -2x² + 4x + 6
(2)以OA的长为直径作圆M, M(3/2, 0), 圆半径 r = 3/2
M与y=-2x+6 (2x + y - 6 = 0)的距离为d = |(3/2)*2 + 0 - 6|/√(2²+1²) = 3/√5 = 3√5/5 < 3/2
圆M与直线AC相交.
换种方法考虑,A在圆上, MA即x轴, 直线AC: y=-2x+6斜率为-2, AC不与x轴垂直, AC不可能与圆M相切, 只能相交.
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我日 这也太难了吧
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