Question

抛物线：y=ax2+bx+c怎么化成顶点式:y=a(x-h)2+b

Answer 1

y=ax^2+bx+c

=a[x^2+(b/a)x]+c

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

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

=a[x+b/(2a)]^2+(4ac-b^2)/(4a)

设-b/(2a)=h,(4ac-b^2)/(4a)=k.

y=a(x-h)^2+k.