Section 3.1: Quadratic Functions and Models

1. Identify whether a quadratic function opens up or down using its coefficients.
2. Identify where a quadratic function obtains a particular value.
3. Express a quadratic function given as \(f(x) = a x^{2} + b x + c\) in standard form \(f(x) = a(x - h)^2 + k\), using the result from the top of page 249 of Stewart, Redlin, and Watson.
4. Define the properties of a global minimum / maximum of a function.
5. Identify when a quadratic function has a global maximum / minimum, and identify where the maximum / minimum occurs and its value.
6. Identify when a quadratic function is an appropriate model for a scientific question, locate the relevant information needed to construct the quadratic function, and identify the relevant characteristics of the quadratic function for answering the original question.