Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
4. Graphing Trigonometric Functions
Graphs of the Sine and Cosine Functions
4: minutes
Problem 71
Textbook Question
Textbook QuestionGraph each function. See Examples 6 – 8. ƒ(x) = 2(x - 2)² - 4
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
4mPlay a video:
Was this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Quadratic Functions
A quadratic function is a polynomial function of degree two, typically expressed in the form f(x) = ax² + bx + c. The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'. Understanding the general shape and properties of parabolas is essential for graphing quadratic functions.
Recommended video:
6:36
Quadratic Formula
Vertex Form of a Quadratic
The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. This form makes it easy to identify the vertex and the direction in which the parabola opens. In the given function, f(x) = 2(x - 2)² - 4, the vertex is at (2, -4), which is crucial for accurately graphing the function.
Recommended video:
6:36
Quadratic Formula
Transformations of Functions
Transformations of functions involve shifting, stretching, or reflecting the graph of a function. In the case of the function f(x) = 2(x - 2)² - 4, the '2' indicates a vertical stretch, while '(x - 2)' represents a horizontal shift to the right by 2 units, and '-4' indicates a vertical shift downward by 4 units. Understanding these transformations helps in accurately sketching the graph.
Recommended video:
4:22
Domain and Range of Function Transformations
Watch next
Master Graph of Sine and Cosine Function with a bite sized video explanation from Nick Kaneko
Start learningRelated Videos
Related Practice