The graph of the quadratic $y = ax^2 + bx + c$ is a parabola that passes through the points $(-1,7)$, $(5,7)$, and $(6,10)$.  What is the $x$-coordinate of the vertex of the parabola?
I notice that the parabola passes through two points with the same $y$-coordinate, $(-1,7)$ and $(5,7)$. This means that the axis of symmetry of the parabola is halfway between $-1$ and $5$, which is $x = 2$. The axis of symmetry is also the $x$-coordinate of the vertex, so the answer is $x = 2$. 