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!  

Consider the graph of the parabola $y=ax^2$. Its vertex is clearly at $(0,0)$. Now, if you replace $x$ with $x-h$ in any equation, its graph gets shifted to the right by a distance of $h$. Similarly, replacing $y$ by $y-k$ shifts the graph up by $k$. If we make both of these substitutions in the above equation of the parabola, its vertex gets shifted to $(h,k)$. The resulting equation after this substitution is $y-k=a(x-h)^2$, or $y=a(x-h)^2+k$.
