Sometimes the expressions that define quadratic functions are written in vertex form. The function $f(x) = (x-3)^2+4$ is in vertex form and is shown in this graph.

The vertex form can tell us about the coordinates of the vertex of the graph of a quadratic function. The expression $(x-3)^2$ reveals that the $x$-coordinate of the vertex is 3, and the constant term, 4, reveals that the $y$-coordinate of the vertex is 4. Here the vertex represents the minimum value of function $f$, and its graph opens upward.

In general, a quadratic function expressed in vertex form is written as $\displaystyle y = a(x-h)^2 + k$. The vertex of its graph is at $(h,k)$. The graph of the quadratic function opens upward when the coefficient, $a$, is positive and opens downward when $a$ is negative.