Question 38528
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:
{{{ graph(300,300, -2,2,-2,30, 6x^2+4) }}}


jon