问题 解答题
已知二次函数y=x2-3x-1的图象经过点M(m,-2),试求代数式m3-m2-4m+2+
3
m2+1
的值.
答案

∵二次函数y=x2-3x-1的图象经过点M(m,-2),则m2-3m+1=0;

∴m2+1=3m,

∴m3-m2-4m+2+

3
m2+1

=m(m2+1)-(m2+1)-5m+3+

1
m

=3(m2-3m+1)+m+

1
m

=

m2+1
m

=

3m
m

=3,即m3-m2-4m+2+

3
m2+1
=3.

单项选择题
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