Glossary Checklist FAQ

Vertex


The vertex of a quadratic function is the lowest or highest point on the graph of that function. If the graph opens upward, the vertex will be the lowest point; if the graph opens downward, then the vertex will be the highest point. What is the connection of \(p\) and \(q\) to the vertex?

Looking back at the Investigation, do you notice anything about the values of \(p\) and \(q\) and the vertex? From examining the last table, you can find that the value of \(p\) is the \(x\)-coordinate of the vertex and the value of \(q\) is the \(y\)-coordinate of the vertex!

Notice the signs in front of \(p\) and \(q\). If the value of \(p\) is negative, then the value within the brackets will become \((x - (-p)) = (x + p) \), whereas if \(q\) is negative, the constant will become \(+(-q) = -q \).



 Key Lesson Marker

The Vertex


Given a quadratic function written in vertex form, \(f(x) = a(x - p)^2 + q \), the vertex is \((p, q) \).

If the graph opens upward, the vertex is the lowest point on the curve.

If the graph opens downward, the vertex is the highest point on the curve.