Question

用配方法把下列二次函数化成y=a(x+m)^2+k形式。

1、y= -2x^2+3x-4
2、y=1/2x^2-x+2

Answer 1

1、y= -2x^2+3x-4=-2（x-3/4）^2-23/8
2、y=1/2x^2-x+2=1/2(x-1)^2+3/2

Answer 2

1、y= -2x^2+3x-4
=-2[x²-(3/2）x+2)
=-2[x²-(3/2)x+(3/4) ²－(3/4) ²+2]
=-2[(x-¾)²-(7/16)]
=-2(x-¾)²+(7/8)

2、y=1/2x^2-x+2
=½(x²-2x+4)
=½(x²-2x+1-1+4]
=½[(x-1) ²+3]
=½(x-1) ²+(3/2)