Identify the coefficients a,b, and c: \(a=-9.5\), \(b=-47.5\), \(c =63\).
substituted \(b = 47.5\) in the formula for finding the vertex.

Let's correct that error and find the correct solution.

\(x=\frac{-b}{2a}\)

\(x=-\frac{47.5}{2*(-9.5)}\)

\(x=-\frac{-47.5}{-19}\)

\(x=-2.5\)

\(y=-9.5*(-2.5)^{2}-47.5*(-2.5)+63\)

\(y=-59.375+118.75+63\)

\(y=122.375\) The vertex is (-2.5, 122.375).

Let's correct that error and find the correct solution.

\(x=\frac{-b}{2a}\)

\(x=-\frac{47.5}{2*(-9.5)}\)

\(x=-\frac{-47.5}{-19}\)

\(x=-2.5\)

\(y=-9.5*(-2.5)^{2}-47.5*(-2.5)+63\)

\(y=-59.375+118.75+63\)

\(y=122.375\) The vertex is (-2.5, 122.375).