Answer
$(0, k)$
Work Step by Step
The vertex form of a quadratic function is $y=a(x-h)^{2}+k$ with a vertex at $(h, k)$. The graph of $f(x)=x^{2}+k$ an be rewritten in vertex form, $f(x)=(x-0)^{2}+k$. Therefore the vertex is at $(0, k)$.
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.