Answer
See below.
Work Step by Step
The maximum value is at $x=-\frac{b}{2a}=-\frac{46}{2\cdot(-1)}=23.$ Hence the maximum value is $f(23)=-(23)^2+46(23)-360=169.$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.