Question

A(1,a)、B(5,b)是直线y=kx+1与抛物线y=x²-4x+m+8的交点.

Answer 1

A(1,a)、B(5,b)是直线y=kx+1与抛物线y=x²-4x+m+8的交点.有

X^2+4X+m+8=kx+1,

x^2-(4+k)x+m+7=0,

x1+x2=1+5=6=4+k,

k=2,

x1*x2=1*5=5=m+7,

m=-2.

y=x^2-4x+6=(x-2)^2+2.

抛物线的顶点坐标为(2,2),对称轴X=2.