Question 23329
First of all, look at the coefficient of the {{{x^2}}} term.  If it is positive, then the parabola is shaped up.  If it is negative, the parabola is shaped down.  The coefficient of the {{{x^2}}} term is 1 so it is shaped up.

Now we have to figure out where the parabola crosses the x axis.  To do this, set the equation equal to zero. 

0 = {{{x^2 + 2*x - 24}}}
0 = (x - 4)(x + 6)
0 = x - 4, 0 = x + 6

So x = 4, x = -6 are our solutions.

Finally, you may need to find the lowest point of this parabola, called the vertex.  To find the x coordinate of the vertex, use the formula x = {{{(-b)/(2*a)}}} where a is the coefficient of the {{{x^2}}} term and b is the coefficient of the {{{x}}} term.  So x = {{{(-2)/(2*1)}}, so x = {{{(-2)/2}}} = -1.  To find the y value that goes with the -1, substitute -1 in for x.  That gives us y = (-1)^2 + 2(-1) - 24 = 1 - 2 - 24 = -25.  So the vertex, or the lowest point of the parabola is (-1, -25).