已知二元一次y=ax方+bx+c满足对称轴为x=1最大值为15与X轴的两交点横坐标的立方和为17求解析式xiexie

Question

已知二元一次y=ax方+bx+c满足对称轴为x=1最大值为15与X轴的两交点横坐标的立方和为17求解析式
xiexie

Answer 1

-b/2a=1
b/a=-2, b=-2a
两交点横坐标：x1,x2
是ax方+bx+c=0的两根
x1+x2=-b/a=2
x1x2=c/a
x1^3+x2^3=(x1+x2)(x1^2-x1x2+x2^2)
=(x1+x2)[(x1+x2)^2-3x1x2]
=2*[4-3(c/a)]=17
c=-(3/2)a
y=ax^2-2ax-(3/2)a=a[x^2-2x-(3/2)]
=a(x-1)^2-(5/2)a