# Properties of a parabola

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Find the domain, range and x intercepts of the following problem approximate to two decimal places of the function

y=3x^2-30x+5

Â© BrainMass Inc. brainmass.com March 6, 2023, 12:49 pm ad1c9bdddfhttps://brainmass.com/math/calculus-and-analysis/properties-parabola-22702

#### Solution Preview

Domain is the set of x values for which the function is defined.

In this function, any value of x will evaluate to a number. Thus the domain of the function is all the real numbers.

As for the range - this is the set of values y can get.

The function is a parabola. Since the coefficient of x^2 is positive, this function has a minima (The maximal value is infinity - just plug in x=infinity or x=-infinity and you'll see).

To calculate the minima, we take the first derivative with respect to x and equate it to zero:

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#### Solution Summary

The properties of a parabola are discussed. The x-intercepts are determined.

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