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# 4.1 quadratic functions and transformations

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### 4.1 quadratic functions and transformations

1. 1. CHAPTER 4 QUADRATIC FUNCTIONSAND EQUATIONS4.1 Quadratic Functions and Transformations Part 1
2. 2. DEFINITIONS A parabola is the graph of a quadratic function.  A parabola is a “U” shaped graph  The parent Quadratic Function is
3. 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. 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. 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. 6. TRANSFORMATIONS – USING VERTEX FORM 
7. 7. EXAMPLE: INTERPRETING VERTEX FORM
8. 8. EXAMPLE: INTERPRETING VERTEX FORM
9. 9. EXAMPLE: INTERPRETING VERTEX FORM
10. 10. EXAMPLE: INTERPRETING VERTEX FORM
11. 11. HOMEWORK Intro to Quadratics WS
12. 12. CHAPTER 4 QUADRATIC FUNCTIONSAND EQUATIONS4.1 Quadratic Functions and Transformations Part 2
13. 13. TRANSFORMATIONS – USING VERTEX FORM 
14. 14. EXAMPLE: GRAPH EACH FUNCTION. DESCRIBEHOW IT WAS TRANSLATED FROM
15. 15. EXAMPLE: GRAPH EACH FUNCTION. DESCRIBEHOW IT WAS TRANSLATED FROM
16. 16. EXAMPLE: GRAPH EACH FUNCTION. DESCRIBEHOW IT WAS TRANSLATED FROM
17. 17. EXAMPLE: GRAPH EACH FUNCTION. DESCRIBEHOW IT WAS TRANSLATED FROM
18. 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. 19. EXAMPLE: WRITE A QUADRATIC FUNCTION TOMODEL EACH GRAPH
20. 20. EXAMPLE: WRITE A QUADRATIC FUNCTION TOMODEL EACH GRAPH
21. 21. HOMEWORK Page 199 #7 – 9, 15 – 18, 29 – 32, 35 – 37 , 41, 49