Patterns

Using the Quadratic Function applet, you probably noticed that parameters a, b, and c all affected the graph differently. You may have noticed the following patterns:

Parameter	Effect on the Graph of
Changing a	Changes the shape of the parabola. When a > 0 the parabola opens up and when a < 0 the parabola opens down.
Changing b	Changes the location of the graph both vertically and horizontally.
Changing c	Changes the location of the graph vertically. Changes the y-intercept of the graph.

The direction of opening can be determined by simply looking at the sign of a. The y-intercept can also be easily determined by simply looking at c. Unfortunately, most other characteristics of the graph are difficult to determine directly from the standard form of a quadratic function. The following table summarizes how to determine characteristics of the graph of a quadratic function given in standard form.

Interpreting
direction of opening	up when a > 0 and down when a < 0
y-intercept	corresponds to the c-value (let x = 0 and determine the value of y)
axis of symmetry	halfway between the x-intercepts of the graph (or roots of the function) — an easy task if the x-intercepts are given
vertex	enter the x-value of the axis of symmetry into the equation of the function to determine the y-value