抛物线y=﹣2/1x²+3/2x+2.设A(a,0)是x轴上一点,若过A可作一条与抛物线有两个到y轴等距离的交点试求a的取值范围.
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![抛物线y=﹣2/1x²+3/2x+2.设A(a,0)是x轴上一点,若过A可作一条与抛物线有两个到y轴等距离的交点试求a的取值范围.](/uploads/image/z/5933356-52-6.jpg?t=%E6%8A%9B%E7%89%A9%E7%BA%BFy%EF%BC%9D%EF%B9%A32%2F1x%26%23178%3B%EF%BC%8B3%2F2x%EF%BC%8B2.%E8%AE%BEA%EF%BC%88a%2C0%EF%BC%89%E6%98%AFx%E8%BD%B4%E4%B8%8A%E4%B8%80%E7%82%B9%2C%E8%8B%A5%E8%BF%87A%E5%8F%AF%E4%BD%9C%E4%B8%80%E6%9D%A1%E4%B8%8E%E6%8A%9B%E7%89%A9%E7%BA%BF%E6%9C%89%E4%B8%A4%E4%B8%AA%E5%88%B0y%E8%BD%B4%E7%AD%89%E8%B7%9D%E7%A6%BB%E7%9A%84%E4%BA%A4%E7%82%B9%E8%AF%95%E6%B1%82a%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4.)
抛物线y=﹣2/1x²+3/2x+2.设A(a,0)是x轴上一点,若过A可作一条与抛物线有两个到y轴等距离的交点试求a的取值范围.
抛物线y=﹣2/1x²+3/2x+2.设A(a,0)是x轴上一点,若过A可作一条与抛物线有两个到y轴等距离的交点
试求a的取值范围.
抛物线y=﹣2/1x²+3/2x+2.设A(a,0)是x轴上一点,若过A可作一条与抛物线有两个到y轴等距离的交点试求a的取值范围.
y=(-1/2)x^2+(2/3)x+2
y=0
x=(2±2√10)/3
A(a,0)
L:y=k(x-a)
(-1/2)x^2+(2/3)x+2=k(x-a)
3x^2+(4+6k)x-12-6ka=0
x1+x2=-(4+6k)/3=0
k=-2/3
3x^2-12-6*(-2/3)a=0
3x^2-12+4a=0
x^2=(12-4a)/3≥0
(2-2√10)/3