将抛物线y=x^2向下平移后,设它与x轴的两个交点分别为,A,B.且抛物线的顶点为c1:若三角形ABC为等边三角形,求此抛物线解析式.2:若三角形ABC为等腰直角三角形,求此抛物线解析式.最好不用三角函
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![将抛物线y=x^2向下平移后,设它与x轴的两个交点分别为,A,B.且抛物线的顶点为c1:若三角形ABC为等边三角形,求此抛物线解析式.2:若三角形ABC为等腰直角三角形,求此抛物线解析式.最好不用三角函](/uploads/image/z/3814857-9-7.jpg?t=%E5%B0%86%E6%8A%9B%E7%89%A9%E7%BA%BFy%3Dx%5E2%E5%90%91%E4%B8%8B%E5%B9%B3%E7%A7%BB%E5%90%8E%2C%E8%AE%BE%E5%AE%83%E4%B8%8Ex%E8%BD%B4%E7%9A%84%E4%B8%A4%E4%B8%AA%E4%BA%A4%E7%82%B9%E5%88%86%E5%88%AB%E4%B8%BA%2CA%2CB.%E4%B8%94%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E9%A1%B6%E7%82%B9%E4%B8%BAc1%3A%E8%8B%A5%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%BA%E7%AD%89%E8%BE%B9%E4%B8%89%E8%A7%92%E5%BD%A2%2C%E6%B1%82%E6%AD%A4%E6%8A%9B%E7%89%A9%E7%BA%BF%E8%A7%A3%E6%9E%90%E5%BC%8F.2%3A%E8%8B%A5%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E4%B8%BA%E7%AD%89%E8%85%B0%E7%9B%B4%E8%A7%92%E4%B8%89%E8%A7%92%E5%BD%A2%2C%E6%B1%82%E6%AD%A4%E6%8A%9B%E7%89%A9%E7%BA%BF%E8%A7%A3%E6%9E%90%E5%BC%8F.%E6%9C%80%E5%A5%BD%E4%B8%8D%E7%94%A8%E4%B8%89%E8%A7%92%E5%87%BD)
将抛物线y=x^2向下平移后,设它与x轴的两个交点分别为,A,B.且抛物线的顶点为c1:若三角形ABC为等边三角形,求此抛物线解析式.2:若三角形ABC为等腰直角三角形,求此抛物线解析式.最好不用三角函
将抛物线y=x^2向下平移后,设它与x轴的两个交点分别为,A,B.且抛物线的顶点为c
1:若三角形ABC为等边三角形,求此抛物线解析式.2:若三角形ABC为等腰直角三角形,求此抛物线解析式.最好不用三角函数)
将抛物线y=x^2向下平移后,设它与x轴的两个交点分别为,A,B.且抛物线的顶点为c1:若三角形ABC为等边三角形,求此抛物线解析式.2:若三角形ABC为等腰直角三角形,求此抛物线解析式.最好不用三角函
1.设抛物线y=x²向下平移a个单位(a > 0),新抛物线的方程为y = x² - a = (x + √a)(x - √a)
顶点为C(0,-a)
y轴为对称轴,AC = BC
A(-√a,0),B(√a,0)
AB = 2√a
BC = AC = √[(√a - 0)² + (0 + a)²] = √(a + a²)
三角形ABC为等边三角形,AB = BC,2√a = √(a + a²),a² = 3a
a = 0 (舍去)或a = 3
抛物线解析式:y = x² - 3
(2)y轴为对称轴,AC = BC,若三角形ABC为等腰直角三角形,只需AC⊥BC即可.
AC的斜率m = (-a - 0)/(0 + √a) = -√a
BC的斜率n = (-a - 0)/(0 - √a) = √a
AC⊥BC,mn = -√a*√a = -1
抛物线解析式:y = x² - 1