How can you tell if a quadratic function has no minimum value?

I have a math test tomorrow %26amp; cannot remember how to recognize if a quadratic function has a minimum/maximum value. I know how to find them I just don't know how to know that they are not there at all.





For example 6+3x-2x squared has no minimum value. But how do I recognize that?How can you tell if a quadratic function has no minimum value?
if the number before x squared ( -2x squared) is negative or has a minus before it, the graph will have a maximum point instead of a minimumHow can you tell if a quadratic function has no minimum value?
One way to tell that a quadratic function has no minimum value is, when put into its vertex form, a is negative. That is, for





f(x) = a(x - h)^2 + k





The vertex is located at (h, k), and


a) if a %26gt; 0, then (h, k) is a minimum


b) if a %26lt; 0, then (h, k) is a maximum.
Sweetheart, that is a linear function.


That's y=x+6.





If I am not mistaken, a parabola has no minimum value if it is shaped like an ';n'; instead of a ';u.'; Which would have what sign (-) (+)?