Why is $(h,k)$ in the vertex formula of a parabola $=a(x-h)^2 +k$ the vertex? Why is it that in the form $y=a(x-h)^2+k$ of a parabola, that $(h,k)$ is the coordinate of the vertex? I am reviewing Algebra and cannot find a reasonable explanation anywhere.The highest level of math I am familiar is with Pre-Calculus. Thanks!  

Since $(x-h)^2$ is always nonnegative, for any value of $x$, it's at its smallest when the thing in parens is zero, i.e., when $x = h$. If $a$ is positive, this will be where the parabola has its minimum, i.e., $x = h$ is the $x$-coord of the vertex. (If $a$ is negative, this is the location of the max, but the same result applies: $x = h$ is the $x$-coord of the vertex). 
At $x = h$, the $y$-value is $a(h-h)^2 + k$< which is just $k$, so the vertex is at location $(h, k). 
