Question 49123
Your teacher is trying to get you to realize that the coefficient of the x^2 term in a quadratic graph determines whether the graph of a parabola will open up (and have a bottom - or minimum value) or open upside down (and have a top - or maximum value).

If the coefficient of the x^2 term is positive, then the graph of the parabola opens upwards, and will have a minimum value.

If the coefficient of the x^2 term is negative, then the graph of the parabola opens downward, and will have a maximum value.

The up or down direction does not depend on either the sign of the x-term or the constant at the end.  These two have other significance which you'll get into later, I'm sure. 

So, to answer your questions:

1. f(x) = x^2 - 9 will open up and have a minimum, since the coefficient of the x^2 is +1.
2. f(x) = 8x - 3x^2 will open down and have a maximum, since the coefficient of the x^2 is -3
3. f(x)=-(3-x)^2

This one is a bit trickier.  You really should simplify the left side by multiplying it out:

-(3-x)^2 = -(3-x)(3-x)  definition of squaring = multiplying by itself
= -(9-6x+x^2)  FOIL it out.
=-9+6x-x^2  distribute the (-).

Therefore, the parabola will open down and have a maximum, since the coefficient of the x^2 is -1

Don't try to just guess on #3!