Answer
No
Work Step by Step
No. The vertex does not depend to $a$ because the vertex of $y=ax^2+c$ is always $(0,c)$, so it depends on $c$.
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.