How do I interpret the graph of a quadratic function?

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How do I interpret the graph of a quadratic function?

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Answer 1 · 2014-08-22T05:00:05

For any graph, we are interested in minimums, maximums, y-intercept, x-intercepts, multiplicity of roots, symmetry, asymptotes, concavity, and end behaviour at $- \infty$ $-oo$ and $\infty$ $oo$ . 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 $\infty$ $oo$ if concavity is up ( $a$ $a$ is positive) and the end behaviour is $- \infty$ $-oo$ if concavity is down ( $a$ $a$ is negative).

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How do I interpret the graph of a quadratic function?

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