Finding and interpreting key feature of quadratics

The Finding and interpreting key feature of quadratics exercise appears under the Algebra I Math Mission and Mathematics II Math Mission. This exercise uses zeros and vertices to solve word problems involving quadratics.

Types of Problems

There is one type of problem in this exercise:

1. Apply the key features of a parabola to the word problem: This problem has a context problem that is modeled with a quadratic equation or function. The user is asked to solve some problems based on the model.

   

   Apply the key features of a parabola to the word problem

Strategies

Knowledge of the quadratic formula can help lead to all elements of this exercise, although vertex form can also be used for some parts.

1. The zeroes can be found by the quadratic formula, which is ${x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}$.
2. The vertex is located at ${(\frac{-b}{2a},f(\frac{-b}{2a})}$.

Real-life Applications

1. The zeroes of a quadratic are used to find many physical interpretations, such as equilibrium prices in supply-demand applications and objects hitting the ground in physics.
2. The vertex is a relative extremum in general, and absolute extremum in the case of a quadratic.
3. The descriptions of problems in this exercise are also real-life applications.