Hello there!
This applet will help you with understanding the relationship between factored and standard form in quadratic equations.

To test your ability to factor a quadratic correctly:
You will be given an equation in standard form. Change the sliders so that the coefficients (a, b, and c) reflect the correct coefficient. Then, factor it in order to obtain the roots. You can then change the sliders on the roots to verify that you factored correctly. If you did factor correctly, then the graph of the parabola will be the same as the original.
To test your ability to change a factored equation to standard form:
You will be given an equation in factored form. Change the sliders so that the coefficients (e and f) to reflect the roots of the equation. Then, expand the quadratic. Change the sliders for the coefficients of the quadratic function in standard form (a, b, and c). If you did expand correctly, then the graph of the parabola will be the same as the original.