This week in precalculus11 I learned about analyzing the quadratic function of the form 
a is the coefficient. It shows the stretch or compression of the parabola. If a > 0 parabola becomes skinnier, and if a < 1the parabola becomes wider. Also, a shows whether the parabola opens up or reflect down.
P represents horizontal translation.
q represents vertical translation.
Here is an example:
