Not surprisingly, vertex form is especially helpful for finding the vertex of a graph of a quadratic function. For example, we can tell that the function, $p$, given by $p(x) = (x-3)^2 + 1$ has a vertex at $(3,1)$.

We also noticed that, when the squared expression $(x-3)^2$ has a positive coefficient, the graph opens upward. This means that the vertex, $(3,1)$, represents the minimum function value, $p(x)$.

The squared term sometimes has a negative coefficient, for instance in $h(x)= \text-2(x+4)^2$. The $x$ value that makes $(x+4)^2$ equal 0 is -4, because $(\text-4+4)^2=0^2=0$. Any other $x$ value makes $(x+4)^2$ greater than 0. But when $(x+4)^2$ is multiplied by a negative number like -2, the resulting expression, $\text-2(x+4)^2$, ends up being negative. This means that the output when $x \neq  \text-4$ will always be less than the output when $x=\text-4$, so function $h$ has its maximum value when $x =\text-4$.