Finding and interpreting key features of quadratics

The  exercise appears under the Algebra I Math Mission. This exercise practices finding and interpreting key features of quadratics.

Types of problems


There is/are one/more type(s) of problem in this exercise:


 * 1) Solve the word problem and type the answers: This problem has a word problem that can be solved by using quadratics, and user is asked to type the answers to questions about the problem (example: What is the lowest depth beneath the water that Guillermo will reach?).

Strategies
Basic knowledge of ... is required for this exercise.


 * 1) For any function given in factored form $$a(x-p)(x-q)$$ we can immediately conclude that:
 * The zeros (or "roots") of the function are the values $$x = \frac{p-q}{2}$$ (this is because parabolas are symmetric about the vertex)
 * If $$a>0$$, then the parabola opens up and the vertex is a minimum.
 * If $$a<0$$, then the parabola opens down and the vertex is a maximum.

Real-life Applications

 * 1) The problems of this exercise can be viewed as real-life applications.