Given the equation of a quadratic function in the form:
[tex]y=ax^2+bx+c[/tex]
Equation: y = x² - 6x + 7
where a = 1, b = -6, and c = 7.
Vertex form of a quadratic function:
[tex]y=a\left(x-h\right)^2+k[/tex]
where (h, k) is the vertex.
To find (h, k):
[tex]\begin{gathered} h=\frac{-b}{2a} \\ \\ h=\frac{6}{2} \\ \\ h=3 \end{gathered}[/tex][tex]\begin{gathered} k=f(3) \\ k=3²-6(3)+7 \\ k=-2 \end{gathered}[/tex]
Vertex = (3, -2)
ANSWER
Vertex form of the quadratic equation:
[tex]y=(x-3)^2-2[/tex]
