Question

How do I interpret the graph of a quadratic function?

Answer 1

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).