已知抛物线y=ax2+bx+c的对称轴为直线x=2,且与x轴交于A、B两点,与y轴交于点C,其中A(1,0),C(0,-3)(1)求抛物线的解析式;(2)若点P在抛物线上运动(点P异于点A).①如图1.当△PBC面积与△
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![已知抛物线y=ax2+bx+c的对称轴为直线x=2,且与x轴交于A、B两点,与y轴交于点C,其中A(1,0),C(0,-3)(1)求抛物线的解析式;(2)若点P在抛物线上运动(点P异于点A).①如图1.当△PBC面积与△](/uploads/image/z/4493666-2-6.jpg?t=%E5%B7%B2%E7%9F%A5%E6%8A%9B%E7%89%A9%E7%BA%BFy%3Dax2%2Bbx%2Bc%E7%9A%84%E5%AF%B9%E7%A7%B0%E8%BD%B4%E4%B8%BA%E7%9B%B4%E7%BA%BFx%3D2%2C%E4%B8%94%E4%B8%8Ex%E8%BD%B4%E4%BA%A4%E4%BA%8EA%E3%80%81B%E4%B8%A4%E7%82%B9%2C%E4%B8%8Ey%E8%BD%B4%E4%BA%A4%E4%BA%8E%E7%82%B9C%2C%E5%85%B6%E4%B8%ADA%EF%BC%881%2C0%EF%BC%89%2CC%EF%BC%880%2C-3%EF%BC%89%EF%BC%881%EF%BC%89%E6%B1%82%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E8%A7%A3%E6%9E%90%E5%BC%8F%EF%BC%9B%EF%BC%882%EF%BC%89%E8%8B%A5%E7%82%B9P%E5%9C%A8%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%B8%8A%E8%BF%90%E5%8A%A8%EF%BC%88%E7%82%B9P%E5%BC%82%E4%BA%8E%E7%82%B9A%EF%BC%89%EF%BC%8E%E2%91%A0%E5%A6%82%E5%9B%BE1%EF%BC%8E%E5%BD%93%E2%96%B3PBC%E9%9D%A2%E7%A7%AF%E4%B8%8E%E2%96%B3)
已知抛物线y=ax2+bx+c的对称轴为直线x=2,且与x轴交于A、B两点,与y轴交于点C,其中A(1,0),C(0,-3)(1)求抛物线的解析式;(2)若点P在抛物线上运动(点P异于点A).①如图1.当△PBC面积与△
已知抛物线y=ax2+bx+c的对称轴为直线x=2,且与x轴交于A、B两点,与y轴交于点C,其中A(1,0),C(0,-3)
(1)求抛物线的解析式;
(2)若点P在抛物线上运动(点P异于点A).
①如图1.当△PBC面积与△ABC面积相等时.求点P的坐标;
②如图2.当∠PCB=∠BCA时,求直线CP的解析式.
(2)若点P在抛物线上运动(点P异于点A).
①如图1.当△PBC面积与△ABC面积相等时.求点P的坐标;
②如图2.当∠PCB=∠BCA时,求直线CP的解析式.
已知抛物线y=ax2+bx+c的对称轴为直线x=2,且与x轴交于A、B两点,与y轴交于点C,其中A(1,0),C(0,-3)(1)求抛物线的解析式;(2)若点P在抛物线上运动(点P异于点A).①如图1.当△PBC面积与△
(1) 对称轴为直线x=2,y = a(x - 2)² + d
x = 1,y = a + d = 0
x = 0,y = 4a + d = -3
a = -1,d = 1
y = -(x - 2)² + 1 = -xy = -x² + 4x - 3 = -(x - 1)(x - 3)
A(1,0),B(3,0)
(2)
①△PBC面积与△ABC面积相等时,AB为共同的底,只须高相同,即P,C纵坐标相等
-x² + 4x - 3 = -3
x = 4 (舍去0)
②BC为角ACP的平分线
AC的解析式:x - y/3 = 1,3x - y - 3 = 0
设CP斜率为k,解析式y = kx - 3,kx - y - 3= 0
B与二者距离相等:
|9 - 0 - 3|/√(9 + 1) = |3k - 0 - 3|/√(k² + 1)
3k² - 10k + 3 = 0
(3k - 1)(k - 3) = 0
k = 1/3 (舍去k = 3,此时CP与AC重合)
直线CP的解析式:y = x/3 - 3
(1) 对称轴为直线x=2, y = a(x - 2)² + d
x = 1, y = a + d = 0
x = 0, y = 4a + d = -3
a = -1, d = 1
y = -(x - 2)² + 1 = -xy = -x² + 4x - 3 = -(x - 1)(x - 3)
A(1, 0), B(3, 0)