Question

把下列二次函数通过配方化为y=a(x-h)^2+k的形式,并写出顶点坐标和对称轴

y=x^2-3x+4
y=2x^2-3x+1

Answer 1

y=x^2-3x+4=(x-3/2)^2+4-9/4=(x-3/2)^2+7/4,顶点为(3/2,7/4),对称轴为x=3/2

y=2x^2-3x+1=2(x^2-3/2x)+1=2(x-3/4)^2+1-9/8=2(x-3/4)^2-1/8,顶点为(3/4,-1/8),对称轴为x=3/4

Answer 2

y=x^2-3x+4
=x^2-3x+9/4-9/4+4
=(x-3/2)^2+7/4

y=2x^2-3x+1
=2x^2-3x+9/8-9/8+1
=2(x^2-3/2x+9/16)-1/8
=2(x-3/4)^2-1/8