Answer
\[x = \frac{{{x_1} + {x_2}}}{2}\]
Work Step by Step
\[\begin{gathered}
The\,equation\,of\,the\,parabola\,having\,zeros\,at\,x = {x_1} \hfill \\
and\,x = {x_2}\,\,is. \hfill \\
\hfill \\
f\,\left( x \right) = c\,\left( {x - {x_1}} \right)\,\left( {x - {x_2}} \right) \hfill \\
\hfill \\
differentiating \hfill \\
\hfill \\
f\left( x \right) = c\,\left( {x - {x_1} + x - {x_2}} \right) \hfill \\
\hfill \\
add \hfill \\
\hfill \\
f\left( x \right) = c\,\left( {2x - {x_1} - {x_2}} \right) \hfill \\
\hfill \\
for\,vertex\,,\,we\,must\,have\,f\left( x \right) = 0\,\,the\,gives \hfill \\
\hfill \\
c\,\left( {2x - \,\left( {{x_1} + {x_2}} \right)} \right) = 0 \hfill \\
\hfill \\
solve\,for\,x \hfill \\
\hfill \\
x = \frac{{{x_1} + {x_2}}}{2} \hfill \\
\end{gathered} \]
