SOLUTION: find domain and range of the function:f(x)=6x^2+4

Question 38528: find domain and range of the function:f(x)=6x^2+4
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
ok...quadratic domain is easy...ANY REAL VALUE OF x.

That said, we now need to find the minimum on the curve since the range is the y-values. Once we have the minimum, then the range is that value or greater.

OK... looking at the equation, the roots (where the curve crosses the x-axis) are symmetrical about the line y=0. By this i mean the roots are of the form -2 and +2 or -10 and +10 etc... Well, they would be like this if the curve crossed the x-axis, but it doesn't... see the graph lower down.

Knowing this about the roots, we then know that the minimum is at x=0, since the minimum of a quadratic is ALWAYS midway between the roots (a quadratic is a symmetric function). So at x=0, we get y=6(0)^2 + 4 --> y=4

So range is ANY REAL VALUE OF y, greater or equal to +4.

And if i plot the graph, you can see this:

jon

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