Introduction

Go to Geogebra - Vertex Form with a and change the a value to a positive number greater than one, then to a fraction between 0 and 1, then to a negative number.

How does the a affect the graph?

In this unit, we will learn how to graph quadratic functions in vertex form. The shifts of the graph will be the same as the shifts that we learned previously with absolute value functions.

Lesson Objectives

Following successful completion of this lesson, students will be able to...

  • Interpret expressions that represent a quantity in terms of its context.
  • Find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
  • Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
  • Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
  • Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
  • Write a function that describes a relationship between two quantities.
  • Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Essential Questions

  • What are the basic families of Function?
  • How does you graph the basic families of functions?
  • What are the properties of each family?
  • How do transfomartions affect the graph of a function?
  • How do transformations affect the equations of a function?

Enduring Understandings

  • Students understand how to solve a variety of functions, and the effects of transformations on functions to describe an object.

The above objectives correspond with the Alabama Course of Study Algebra II with Statistics standards: 15, 16, 17, 20, and 20a.