Answer :
Answer:
[tex]\boxed{\bold{f(x)=(x-9)^2+2}}[/tex]
Step-by-step explanation:
[tex]f(x)=a(x-h)^2+k\qquad\qquad h=\dfrac{-b}{2a}\,,\ \ k=f(h)\\\\\\f(x)=x^2-18x+83\quad\implies\quad a=1\,,\ b=-18\\\\h=\dfrac{-(-18)}{2\cdot1}=\dfrac{18}{2}=9\\\\h=f(3)=9^2-18(9)+83=81-162+83=2\\\\\\ \underline{f(x)=(x-9)^2+2}[/tex]