Math 092 Module 4 Lesson 1a - Quadratic functions with transformations

This is Math 092 Module 4 Lesson 1a. It introduces quadratic functions from their basic form of x squared, using transformations to develop the general vertex form of a quadratic function (or parabola). The focus is on identifying how a quadratic function can be graphed as based on function transformations and observing features of quadratic functions that may be useful in analysis. See the timestamps below to refer to specific parts of the lesson.

0:00 Introducing quadratic function models (in contrast to linear function models)
1:24 Basic form of a quadratic function
3:54 Line of symmetry in a quadratic function
4:32 Quadratic function with a shift
9:06 Left and right transformations
12:19 Flip transformations
13:25 Up and down transformations
14:15 Vertex form of a quadratic function (or parabola)
16:02 General vertex form of a quadratic function (or parabola)
16:34 Anatomy of a quadratic function (or parabola)
18:14 Quadratic practice example 1 - graphing a quadratic function (or parabola), and identifying its vertex, domain and range
26:40 Quadratic practice example 2 - graphing a quadratic function (or parabola), and identifying its vertex, domain and range
28:29 Quadratic practice example 3 - graphing a quadratic function (or parabola) when it is NOT in vertex form - using completing the square
33:42 Vertex formula
34:40 Identifying vertex in an application problem