<p>Name: ______</p><p>TRANSFORMATIONS of the Quadratic function: y = x2 - Part I</p><p>A. Graph the quadratic function: 2 yx Describe the basic shape of this graph:</p><p>______</p><p>What are the coordinates of the vertex of this graph?</p><p>______</p><p>B. Keep this quadratic function in y1, and graph each of the following: 1. y = (x – 3)2 2. y = (x – 2)2 3. y = (x – 1)2</p><p>Vertex:_____ Vertex:_____ Vertex:_____</p><p>C. Compare graphs 1, 2, and 3 with the “parent-graph” ( y= (x)2. How are “the kids” different? How are they the same?</p><p>D. Investigate the behavior of some other “kids” by graphing each of the following functions: </p><p>4.y = (x + 3)2 5. y = (x + 2)2 6. y = (x + 1)2</p><p>Vertex:_____ Vertex:_____ Vertex:_____</p><p>E. Compare graphs 4, 5, 6 with the “parent-graph” ( y= x2). How are “the kids” different? How are they the same? F. Next, investigate the graphs of the following 6 functions:</p><p>7. y = x2 - 3 8. y = x2 - 2 9. y = x2 - 1 </p><p>Vertex:______Vertex:______Vertex:______</p><p>10. y = x2 + 3 11. y= x2 + 2 12. y = x2 + 1</p><p>Vertex:_____ Vertex:_____ Vertex:_____</p><p>G. In a short paragraph, describe the similarities and differences between graphs 1-6 and 7-12. </p><p>H. If you did not have access to a graphing calculator, how might you explain to a new student in the class how to draw the graphs of each of the following functions: 13. y = x2 + 4 14. y = (x – 8)2</p><p>15. y = (x + 12)2 16. y = x2 - 7</p><p>I. Without use of a graphing calculator, how might you draw the graph of each of these functions? 17. y = (x – 3)2 + 2 18. y = (x + 1)2 - 4</p><p>19. y = (x + 2)2 + 3 20. y = (x – 2)2 - 1 TRANSFORMATIONS of the Quadratic Function: y = x2 - Part II</p><p>A. Graph the Quadratic function: (remember to keep this graph in y1) 2 yx Describe the basic shape of this graph:</p><p>______</p><p>What are the coordinates of the vertex of this graph?</p><p>______Vertex:_____</p><p>B. Draw the graph of the following function: y = - x2</p><p>Compare this graph with the “parent” graph in part A.</p><p>______</p><p>Why do you think this graph is called a “vertical reflection” of the quadratic function? </p><p>Vertex:______</p><p>C. Now try graphing the following quadratic function equations. </p><p>1. y = - x2 + 1 2. y = - x2 - 2</p><p>Vertex:____ Vertex:_____</p><p>3. y = - (x – 3)2 4. y = - (x + 4)2</p><p>Vertex:_____ Vertex:_____</p><p>D. Explain what happens to the graph if the quadratic is multiplied by a negative. E. Now we’re going to get tricky! - Graph the following: 5. y = 2x2 Describe the similarities and differences between the graph of y = |x| and this graph.</p><p>______</p><p>______</p><p>Vertex:_____</p><p>F. Now try graphing the following quadratic equations. </p><p>6. y = ½ x2 7. y = (3/2) x2 8. y = 0.75x2</p><p>Vertex:_____ Vertex:_____ Vertex:_____</p><p>G. What is the effect on the graph of multiplying the quadratic function by a positive number that is greater than 1?</p><p>H. What is the effect on the graph of multiplying the quadratic function by a positive number that is less than 1?</p><p>I. PUTTING IT ALL TOGETHER ! In the following functions, I have combined the transformations on the quadratic function that you just discovered. Try graphing the following functions without a graphing calculator, then use your calculator to check your answer. </p><p>9. y = (x – 1)2 + 2 10. y = - (x + 3)2 11. y = 3(x)2 - 6</p><p>Vertex:_____ Vertex:_____ Vertex:_____ Homework: 4. y = -2(x – 4)2 5. f(x) = ½ (x – 2)2 – 1 6. g(x) = - (x + 2)2 + 5</p><p>Show your tables here:</p><p>Make a conjecture about functions that come in the form: y = a(x – h)2 + k. Explain the effect of a, h and k on the quadratic function graph.</p>