Modeling problems with quadratic functions can be very difficult. It is essentially solving a word problem via determining the relationships between the variables presented in the problem.
To solve these types of problems:
Firstly remember that quadratics work for 2 missing variables, this is important to remember when determining the variables.
Next, to start solving, determine the variables in the problem and then any other information the question may be disguising. Be aware of different terminology that can indicate different information for example, Sum, Product, greatest, least, etc…
Next, identifying the relationship between these variables will allow you to conduct the rest of the problem. After the relationships between values and variables is established it’s simply a matter of manipulation formulas and information to produce the answer you’re looking for. Factored form is often a good form to use because it will allow you to find the zeros of the equation.