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# 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

##### Solution Summary

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

##### 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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