如图,抛物线y=ax²-x-1.5与X轴正半轴交于点A(3,0),以OA为边在X轴上做正方形OABC,延长CB交抛物线于点D,再与BD为边向上作正方形BDEF.(1)求a (2)求F坐标.
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![如图,抛物线y=ax²-x-1.5与X轴正半轴交于点A(3,0),以OA为边在X轴上做正方形OABC,延长CB交抛物线于点D,再与BD为边向上作正方形BDEF.(1)求a (2)求F坐标.](/uploads/image/z/5634474-42-4.jpg?t=%E5%A6%82%E5%9B%BE%2C%E6%8A%9B%E7%89%A9%E7%BA%BFy%3Dax%26%23178%3B-x-1.5%E4%B8%8EX%E8%BD%B4%E6%AD%A3%E5%8D%8A%E8%BD%B4%E4%BA%A4%E4%BA%8E%E7%82%B9A%EF%BC%883%2C0%EF%BC%89%2C%E4%BB%A5OA%E4%B8%BA%E8%BE%B9%E5%9C%A8X%E8%BD%B4%E4%B8%8A%E5%81%9A%E6%AD%A3%E6%96%B9%E5%BD%A2OABC%2C%E5%BB%B6%E9%95%BFCB%E4%BA%A4%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%BA%8E%E7%82%B9D%2C%E5%86%8D%E4%B8%8EBD%E4%B8%BA%E8%BE%B9%E5%90%91%E4%B8%8A%E4%BD%9C%E6%AD%A3%E6%96%B9%E5%BD%A2BDEF.%EF%BC%881%EF%BC%89%E6%B1%82a%E3%80%80%E3%80%80%E3%80%80%E3%80%80%EF%BC%882%EF%BC%89%E6%B1%82F%E5%9D%90%E6%A0%87.)
如图,抛物线y=ax²-x-1.5与X轴正半轴交于点A(3,0),以OA为边在X轴上做正方形OABC,延长CB交抛物线于点D,再与BD为边向上作正方形BDEF.(1)求a (2)求F坐标.
如图,抛物线y=ax²-x-1.5与X轴正半轴交于点A(3,0),以OA为边在X轴上做正方形OABC,延长CB交抛物线于点D,再与BD为边向上作正方形BDEF.
(1)求a (2)求F坐标.
如图,抛物线y=ax²-x-1.5与X轴正半轴交于点A(3,0),以OA为边在X轴上做正方形OABC,延长CB交抛物线于点D,再与BD为边向上作正方形BDEF.(1)求a (2)求F坐标.
答:
(1)
把点A(3,0)代入抛物线方程y=ax²-x-1.5得:
9a-3-1.5=0
a=1/2
(2)
抛物线方程为:y=x²/2-x-3/2
OA=OC=CB=3
所以点C(0,3),B(3,3),设点D为(d,3)代入抛物线方程得:
d^2/2-d-3/2=3
解得d=1+√10(d=1-√10不符合题意舍去)
所以点D为(1+√10,3)
BF=BD=1+√10-3=√10-2
故点F(3,3+√10-2),即F(3,1+√10)
(1)y=ax²-x-1.5
A(3,0)代入
0=9a-3-1.5
a=0.5
(2)∵正方形OABC,0A=3
∴当y=3时代入
3=0.5x²-x-1.5
x1= 1-根号10(不符合图像,舍去) ...
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(1)y=ax²-x-1.5
A(3,0)代入
0=9a-3-1.5
a=0.5
(2)∵正方形OABC,0A=3
∴当y=3时代入
3=0.5x²-x-1.5
x1= 1-根号10(不符合图像,舍去) x2=根号10+1
∴ D(根号10+1,3)
∵AF=DC
∴F(3,根号10+1)
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