Answer:
[tex]\text{The vertex form is }y=(x-3)^2-2[/tex]
Step-by-step explanation:
Given a quadratic equation [tex]y=x^2-6x+7[/tex]
we have to write the equation in vertex form.
Comparing given equation with the standard equation [tex]y=ax^2+bx+c[/tex], we get
a=1, b=-6 and c=7
[tex]h=x_{vertex}=\frac{-b}{2a}=\frac{6}{2}=3[/tex]
Substitute the value of x in given equation,
[tex]k=y_{vertex}=1(3)^2-6(3)+7=9-18+7=-2[/tex]
Now, put above values in vertex form of quadratic equation i.e
[tex]y=a(x-h)^2+k[/tex]
[tex]y=1(x-3)^2-2[/tex]
Hence, the vertex form is
[tex]y=(x-3)^2-2[/tex]