Glossary Checklist FAQ

Direction of Opening


As you have seen, the graphs of quadratic functions either open upward or downward. What determines the direction of opening? The sign of \(a\) determines whether a function opens upward or downward, which corresponds to the vertex occurring at a maximum or a minimum. If \(a\) is positive, the function opens upward, and the \(y\)-coordinate of the vertex is the minimum value. If \(a\) is negative, the function opens downward, and the \(y\)-coordinate of the vertex is the maximum value.




 Key Lesson Marker

Direction of Opening


For quadratic functions of the form \(f(x) = a(x - p)^2 + q \):

\(a > 0\) indicates the graph of the function opens upward, and the graph has a minimum at \(y = q\)

\(a < 0\) indicates the graph of the function opens downward, and the graph has a maximum at \(y = q\)

The direction of opening will also affect the range as well as the number of \(x\)-intercepts.