A) To factor a quadratic equation, standard form is the better form to use because it is easier to pull out a common factor from.
b) To graph a parabola, it is better to use vertex form so that you will know what point to graph as the vertex of the parabola.
c) To identify the vertex, maximum and minimum, it is better to use vertex form because the vertex form will give the values of the coordinates for the vertex. Then, you can use the equation to find the mininmum or maximum. If the graph is negative, it will have a maximum because it points downward infinitely. If the equation is positive, the graph will have a minimum because the graph points upward infinitely.
d) Standard form is easier to use when trying to solve using the quadratic formula because it is easier to see what the coeffiecnts and constants are to plug in for a b and c.
Let's say you want to compute the probability where converges in distribution to , and follows a normal distribution. The normal approximation (without the continuity correction) basically involves choosing such that its mean and variance are the same as those for .
Example: If is binomially distributed with and , then has mean and variance . So you can approximate a probability in terms of with a probability in terms of :