4.1 quadratic functions and transformations
- 1. CHAPTER 4 QUADRATIC FUNCTIONS AND EQUATIONS 4.1 Quadratic Functions and Transformations Part 1
- 2. DEFINITIONS A parabola is the graph of a quadratic function. A parabola is a “U” shaped graph The parent Quadratic Function is
- 3. DEFINITIONS The vertex form of a quadratic function makes it easy to identify the transformations The axis of symmetry is a line that divides the parabola into two mirror images (x = h) The vertex of the parabola is (h, k) and it represents the intersection of the parabola and the axis of symmetry.
- 4. REFLECTION, STRETCH, AND COMPRESSION The determines the “width” of the parabola If the the graph is vertically stretched (makes the “U” narrow) If the graph is vertically compressed (makes the “U” wide) If a is negative, the graph is reflected over the x– axis
- 5. MINIMUM AND MAXIMUM VALUES The minimum value of a function is the least y – value of the function; it is the y – coordinate of the lowest point on the graph. The maximum value of a function is the greatest y – value of the function; it is the y – coordinate of the highest point on the graph. For quadratic functions the minimum or maximum point is always the vertex, thus the minimum or maximum value is always the y – coordinate of the vertex
- 6. TRANSFORMATIONS – USING VERTEX FORM
- 7. EXAMPLE: INTERPRETING VERTEX FORM
- 8. EXAMPLE: INTERPRETING VERTEX FORM
- 9. EXAMPLE: INTERPRETING VERTEX FORM
- 10. EXAMPLE: INTERPRETING VERTEX FORM
- 11. HOMEWORK Intro to Quadratics WS
- 12. CHAPTER 4 QUADRATIC FUNCTIONS AND EQUATIONS 4.1 Quadratic Functions and Transformations Part 2
- 13. TRANSFORMATIONS – USING VERTEX FORM
- 14. EXAMPLE: GRAPH EACH FUNCTION. DESCRIBE HOW IT WAS TRANSLATED FROM
- 15. EXAMPLE: GRAPH EACH FUNCTION. DESCRIBE HOW IT WAS TRANSLATED FROM
- 16. EXAMPLE: GRAPH EACH FUNCTION. DESCRIBE HOW IT WAS TRANSLATED FROM
- 17. EXAMPLE: GRAPH EACH FUNCTION. DESCRIBE HOW IT WAS TRANSLATED FROM
- 18. TRANSFORMATIONS – USING VERTEX FORM Writing the equations of Quadratic Functions: 1. Identify the vertex (h, k) 2. Choose another point on the graph (x, y) 3. Plug h, k, x, and y into and solve for a 4. Use h, k, and a to write the vertex form of the quadratic function
- 19. EXAMPLE: WRITE A QUADRATIC FUNCTION TO MODEL EACH GRAPH
- 20. EXAMPLE: WRITE A QUADRATIC FUNCTION TO MODEL EACH GRAPH
- 21. HOMEWORK Page 199 #7 – 9, 15 – 18, 29 – 32, 35 – 37 , 41, 49