Given a quadratic equation in the form y = ax2 +bx +c , and four choices of graphs representing that equation, how can you tell which choices could be eliminated right away by looking at the equation and looking at the graphs and doing some minimal c?

1. Start by putting x = 0 in the equation this gives  y = c at x = 0. This will eliminate some of the choices.  2 . Now put x = infinity. => y = a x (infinity)^2. This means only those graphs which go to infinity for large values of x can be the correct one. Note here that if a is negative the curves go to - infinity for infinite x.  3. Another trick is to look at the graphs and see where the curves intersect the x - axis i.e. The roots of the equation or the values of x for which y = 0. Put these values in the given expression to see if these satisfy it.  4. Remember, these graphs will always be parabolas. So you can chuck any circles, ellipses etc.