用配方法推導一元二次方程ax2+bx+c=0(a≠0)的求根公式.
解:ax
2+bx+c=0(a≠0),
方程左右兩邊同時除以a得:x
2+

x+

=0,
移項得:x
2+

x=-

,
配方得:x
2+

x+

=

-

=

,即(x+

)
2=

,
當b
2-4ac≥0時,x+

=±

=±

,
∴x=

.
分析:由a不為0,在方程左右兩邊同時除以a,并將常數(shù)項移到方程右邊,方程左右兩邊都加上一次項系數(shù)一半的平方,左邊化為完全平方式,右邊通分并利用同分母分式的減法法則計算,當b
2-4ac≥0時,開方即可推導出求根公式.
點評:此題考查了一元二次方程的求根公式,以及配方法的應用,學生在開方時注意b
2-4ac≥0這個條件的運用.