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