.
The minimum of a quadratic function of the general form
y = ax^2 + bx + c
having positive coefficient at x^2 is achieved at x = .
In your case a= 3, b= -72, c= 576 and the minimum is achieved at
x = = = 12 miles.
Answer. The pollution is the least at x = 12 miles from factory A toward factory B.
-----------------
On finding the maximum/minimum of a quadratic function see the lessons
- HOW TO complete the square to find the minimum/maximum of a quadratic function
- Briefly on finding the minimum/maximum of a quadratic function
- HOW TO complete the square to find the vertex of a parabola
- Briefly on finding the vertex of a parabola
- OVERVIEW of lessons on finding the maximum/minimum of a quadratic function
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this textbook under the topic "Finding minimum/maximum of quadratic functions".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.