How do I interpret the graph of a quadratic function?

1 Answer
Aug 22, 2014

For any graph, we are interested in minimums, maximums, y-intercept, x-intercepts, multiplicity of roots, symmetry, asymptotes, concavity, and end behaviour at #-oo# and #oo#. When you start calculus, you are also interested in inflection points.

For quadratics:

  • 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).