Question

Write y=x^2-18x+83 in vertex form. Then identify the vertex.​

Answer 1

`\boxed{\bold{f(x)=(x-9)^2+2}}`

Explanation:

`f(x)=a(x-h)^2+k\qquad\qquad h=(-b)/(2a)\,,\ \ k=f(h)\\\\\\f(x)=x^2-18x+83\quad\implies\quad a=1\,,\ b=-18\\\\h=(-(-18))/(2\cdot1)=(18)/(2)=9\\\\h=f(3)=9^2-18(9)+83=81-162+83=2\\\\\\ \underline{f(x)=(x-9)^2+2}`