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