Question

如图,二次函数y=1/2x^2-3/2x+1的图像与y轴交于A点,与x轴交于B、C两点,M为函数图像对称轴上一动点,

Answer 1

y=(1/2)x^2-(3/2)x+1

=(1/2)(x-2)(x-1)

A(0,1)

B(1,0) C(2,0)

对称轴x=(3/2)/2*(1/2)=3/2

M(3/2,y0)

直线AC y=(1/-2)(x-2)=(-1/2)x+1

x=3/2,y=(1/4)

M(3/2,1/4)时

|MA-MC|最大=|AC|=√5

My≠1/4

|MA-MC|