Question

怎样用配方法将二次函数y＝ax²+bx+c化成y＝a(x-h)²+k的形式?

Answer 1

y＝ax²+bx+c

=a(x^2+b/a*x)+c

=a(x^2+(b/a)x+(b/(2a))^2 - (b/(2a))^2 ) +c

=a( (x^2+(b/a)x+(b/(2a))^2) - (b/(2a))^2 ) +c

=a( (x+b/(2a))^2 - (b/(2a))^2 ) +c

=a(x+b/(2a))^2 - a(b/(2a))^2 ) +c

=a(x+b/(2a))^2 - b^2/(4a) +c

这里：h= -b/(2a),k= - b^2/(4a) +c