How do I interpret the graph of a quadratic function?
For any graph, we are interested in minimums, maximums, y-intercept, x-intercepts, multiplicity of roots, symmetry, asymptotes, concavity, and end behaviour at
- You will find an absolute minimum or maximum but not both.
- You will always find a y-intercept but not necessarily any x-intercepts.
- Since a quadratic only has up to 2 roots, multiplicity can only be 1 or 2.
- There will always be horizontal symmetry on the vertical line that passes through the vertex.
- There are no asymptotes.
- It will be either concave up or down.
- The end behaviour is
#oo#if concavity is up ( #a#is positive) and the end behaviour is #-oo#if concavity is down ( #a#is negative).