We have to find the vertex and write the equation in vertex form.
The equation is:
[tex]f(x)=x^2-6x+17[/tex]We start by calculating the coordinates of the vertex (h,k):
[tex]h=-\frac{b}{2a}=\frac{-(-6)}{2\cdot1}=\frac{6}{2}=3[/tex][tex]k=f(h)=3^2-6\cdot3+17=9-18+17=8[/tex]The vertex form is:
[tex]\begin{gathered} f(x)=a(x-h)^2+k \\ f(x)=(x-3)^2+8 \end{gathered}[/tex]Answer:
Vertex: (3,8)
Vertex form: f(x)=(x-3)^2+8
