若直线y=-2x与抛物线y=ax²-2相交于点A,已知A点的坐标为A(-2,b),抛物线y=ax²-2的顶点为B.(1)求此抛物线的解析式;(2)求△OAB的面积
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/22 07:33:32
![若直线y=-2x与抛物线y=ax²-2相交于点A,已知A点的坐标为A(-2,b),抛物线y=ax²-2的顶点为B.(1)求此抛物线的解析式;(2)求△OAB的面积](/uploads/image/z/8660737-1-7.jpg?t=%E8%8B%A5%E7%9B%B4%E7%BA%BFy%3D-2x%E4%B8%8E%E6%8A%9B%E7%89%A9%E7%BA%BFy%3Dax%26%23178%3B-2%E7%9B%B8%E4%BA%A4%E4%BA%8E%E7%82%B9A%2C%E5%B7%B2%E7%9F%A5A%E7%82%B9%E7%9A%84%E5%9D%90%E6%A0%87%E4%B8%BAA%EF%BC%88-2%2Cb%EF%BC%89%2C%E6%8A%9B%E7%89%A9%E7%BA%BFy%3Dax%26%23178%3B-2%E7%9A%84%E9%A1%B6%E7%82%B9%E4%B8%BAB.%EF%BC%881%EF%BC%89%E6%B1%82%E6%AD%A4%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%E6%B1%82%E2%96%B3OAB%E7%9A%84%E9%9D%A2%E7%A7%AF)
若直线y=-2x与抛物线y=ax²-2相交于点A,已知A点的坐标为A(-2,b),抛物线y=ax²-2的顶点为B.(1)求此抛物线的解析式;(2)求△OAB的面积
若直线y=-2x与抛物线y=ax²-2相交于点A,已知A点的坐标为A(-2,b),抛物线y=ax²-2的顶点为B.(1)求此抛物线的解析式;
(2)求△OAB的面积
若直线y=-2x与抛物线y=ax²-2相交于点A,已知A点的坐标为A(-2,b),抛物线y=ax²-2的顶点为B.(1)求此抛物线的解析式;(2)求△OAB的面积
(1)∵点A(-2,b)在直线y=-2x上
∴b=-2×(-2)=4
∵点A(-2,4)在抛物线y=ax²-2上
∴4=4a-2,a=3/2
则抛物线的解析式为y=3/2 x²-2
(2)∵抛物线y=3/2x²-2的顶点为B(0,-2)
∴S△OAB=1/2×2×2=2