D. Analyzing Quadratic Functions Expressed in Vertex Form

A quadratic function in vertex form, , allows you to determine the coordinates of the vertex quickly from the h and k values.

Change the h and k values to see how they are related to the vertex of the graph.

Vertex form applet (Created with GeoGebra)

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

You might have noticed, when using the Vertex Form applet, that the vertex of the graph of a quadratic function expressed in the form occurs at (h, k). Knowing the vertex also allows you to quickly determine the equation of the axis of symmetry and the coordinates of the maximum or minimum.

Since the vertex occurs at (h, k), the equation of the axis of symmetry is x = h, and the maximum or minimum value of the function is k. The a-value will help you determine the direction of opening just as it did in standard form.

This a-value also allows you to determine whether the graph has a maximum or minimum.

Interpreting
vertex (h, k)
axis of symmetry x = h
maximum/minimum y-value k
direction of opening up when a > 0 and down when a < 0
y-intercept let x = 0 and determine the value of y