The solution to the inequality
\[y = -x^2 + ax + b \le 0\]is $(-\infty,-3] \cup [5,\infty).$  Find the vertex of the parabola $y = -x^2 + ax + b.$
Question:
The solution to the inequality
\[y = -x^2 + ax + b \le 0\]is $(-\infty,-3] \cup [5,\infty).$  Find the vertex of the parabola $y = -x^2 + ax + b.$
Answer:
Let's think step by step.

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The solution to the inequality
\[y = -x^2 + ax + b \le 0\]is $(-\infty,-3] \cup [5,\infty).$  Find the vertex of the parabola $y = -x^2 + ax + b.$
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