Quadratic Functions

In this lesson on quadratic functions, students will learn about the algebraic form for a quadratic model and its parameters, including whether those parameters have any meaning in the context of the functional relationship. Though A, B, and C all serve a role in the quadratic form, B is really the only parameter that can be interpreted as linear, and A has no direct relationship to the rate of change. However, the sign of A can reveal important information about the minimum or maximum of the quadratic function. By using input/output pairs, students can find a unique parabola that fits their data and determine the corresponding parameters.

Be familiar with and recognize the algebraic form for a quadratic model, including the corresponding parameters and if those parameters have any meaning in the context of the functional relationship (e.g. does a parameter control the initial value, rate of change (shape), decreasing or increasing (flip), max/min, limiting values, etc.).

• What are the parameters of a quadratic model?
• What is a quadratic model?
• What is a non-linear model?
• What happens in a model if you do not have a constant rate of change?
• What is standard form for a quadratic function?
• What is vertex form for a quadratic function?
• How do you find the initial value of a quadratic function?
• What is the linear parameter and what is the quadratic parameter in a quadratic model?
• How can you tell whether a quadratic function opens up or down from the function?
• How do you find the values of parameters in a quadratic model?
• How can you write a quadratic function given two points (2, 10) and (3, 8) and an initial value of 0?
• How can you use a TI graphing calculator to model a quadratic function by doing a quadratic regression?
• How many points do you need to specify a quadratic function?