1. Consider the function: f(x) = 2|x – 2| + 1 1. Does the graph of the function open up or down? 2. Is the graph of the function wider, narrower, or the same width as y = |x|? 3. What is the vertex of the graph? 4. What is the line of symmetry for the graph? 5. What numbers would you put in the table to complete the graph? Algebra II 1

2. Transformations of Quadratic Functions

3. Algebra II 3

4.  A quadratic function has a squared term in it, or a degree of two.  The graph of a quadratic makes a “U” shape called a parabola.  Vertex of a parabola: the maximum or minimum of a parabola.  Vertex form: y = a(x – h) 2 + k Algebra II 4

5. 5 a: stretches, shrinks, reflects h: translates left/right k: translates up/down

6. y = a(x – h) 2 + k  Vertex: (opposite of h, same as k)  Axis of symmetry (AOS): x = opposite of h.  a: determines the direction the graph opens, and the width of the graph  a > 0 opens up  a < 0 opens down  |a| < 1 wider than x 2  |a| > 1 narrower than x 2  |a| = 1 same width as x 2 Algebra II 6

7. 7 Parent Function: F(x) = x 2 Shift Right 1 Down 2 G(x) = (x – 1) 2 – 2

8.  h is INSIDE with the x  It moves the graph the opposite direction left or right 8 Algebra II

9.  k is OUTSIDE with the x  It moves the graph the same direction up or down 9 Algebra II

10.  Negate y  Negative is outside of the parenthesis  Reflects over x axis 10 Algebra II

11.  Negate x  Negative is inside of the parenthesis  Reflects over y axis 11 Algebra II

12.  Coefficient is in side of the parenthesis  Reciprocal 12 Algebra II

13.  Coefficient is outside of the parenthesis 13 Algebra II

14. 14 Algebra II  Shift up four

15. 15 Algebra II  Shift right one  Shift down 3

16. 16 Algebra II  Reflect over x axis  Shift left 9

17. 17 Algebra II  Shift down 7

18. 18 Algebra II  Vertical shrink of 1/3  Shift down 6

19. 19 Algebra II  Horizontal shrink of 1/4  Reflect over y axis

20.  Describe the transformation of the graph from the parent function.  Reflect over x axis  Vertical stretch 10  Shift right 5 up 7  Identify the vertex.  Vertex: (5, 7) 20 Algebra II