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A quadratic function: f(x) = ax2 + bx + c = 0, where a ≠ 0.

Domain: {x| x is a real number}, or in the interval notation, (-∞, ∞).

Range:

If a > 0, {y| y ≥ f(-b/2a), the y-coordinate of the vertex} or [f(-b/2a), ∞).

If a < 0, {y| y ≤ f(-b/2a), the y-coordinate of the vertex} or (-∞, f(-b/2a)].

* * * * *

Alternative answer:

The domain is anything you chose it to be. For example, the integers between 2.5 and 4.7 (ie 3 and 4) and the real numbers between 4.8 and 5.0.

Then the range would be the values of f(x) which corresponded to the values of x in the domain.

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Q: How do you find the domain and range given a quadratic function?
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