# quadrartic function what is the domain and range f(x)=x^2-8x+12must show work

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Expert Answers

degeneratecircle | Certified Educator

The domain is the largest set of allowable inputs. There is no possible division by zero or square rooting of negative numbers, etc., so all real numbers are allowable inputs. In other words, the domain is the set of all real numbers.

As for the range, one way to proceed is to complete the square.

`x^2-8x+12=(x-4)^2-4.`

The smallest value of `(x-4)^2-4` is -4, and since the graph is a parabola opening up (because the coefficient of the `x^2` term is positive), the function takes on all values greater than or equal to -4. In other words, the range is `[-4,oo)`.

Here's the graph so we can check.

**The domain is `RR` ****and the range is** `[-4,oo)`