<p> Name:______Date:______Period:______</p><p>Graphing Investigation - Reflect and Apply:</p><p>Chart 1: Use a graphing calculator to sketch the graphs of parabolas in the form y ax 2 , and we see how the value of a affects the shape of the graph.</p><p>Is the In the same Does the vertex the viewing window, is Value of parabola highest or the graph the Function Sketch a in open up lowest point same, narrower, y ax 2 or down? of the or wider then 2 graph? y ax ?</p><p> y x 2 1 Up Lowest The same</p><p> y 1 x 2</p><p> y 6 x 2</p><p> y 6 x 2</p><p> y 0.3 x 2</p><p> y 0.3 x 2</p><p>SATEC/Algebra II/Quadratic F’ns/Parameter Changes/ 0e56e1158b119d4c41b798cac9ed7034.doc/Rev. 07-01 Page 1 of 9 Use the information from CHART 1 to help you answer the following questions:</p><p>1. Does changing the value of a in the general equation y  ax 2 affect whether the </p><p> parabola opens up or down? If so, how? </p><p>2. Does changing the value of a affect the location of the vertex? If so, how? </p><p>3. How does the value of a indicate when the vertex is the highest point or lowest </p><p> point of the parabola? </p><p>4. Does the value of a indicate whether the parabola is narrower or wider than the</p><p> graph y  x 2 or y  1x 2 ? If so, how? </p><p>CHART 2: Use a graphing calculator to sketch the graphs of parabolas in the form y ax2  c , and we see how the value of c affects the graph.</p><p>SATEC/Algebra II/Quadratic F’ns/Parameter Changes/ 0e56e1158b119d4c41b798cac9ed7034.doc/Rev. 07-01 Page 2 of 9 Compared to Does the y 1 x 2 , is Value of c Coordinates parabola this graph the Function Sketch in of the 2 open up same, y ax  c vertex or down? narrower, or wider?</p><p> y1 x 2  0</p><p> y1 x 2  2</p><p> y1 x 2  4</p><p> y1 x 2  8.5</p><p>Use the information from CHART 2 to help you answer the following questions: SATEC/Algebra II/Quadratic F’ns/Parameter Changes/ 0e56e1158b119d4c41b798cac9ed7034.doc/Rev. 07-01 Page 3 of 9 5. How does changing the value of c affect the graphs in the chart? </p><p>6. Does changing the value of c change the location of the vertex of the parabola? </p><p>If so, in what way? </p><p>7. If c is greater than 0, what happens to the graph? </p><p>8. If c is less than 0, what happens to the graph? </p><p>9. Make up an equation whose graph will be a parabola between the graphs of the </p><p> equations y  1x 2 and y  1x 2  9 . </p><p>SATEC/Algebra II/Quadratic F’ns/Parameter Changes/ 0e56e1158b119d4c41b798cac9ed7034.doc/Rev. 07-01 Page 4 of 9 Graph each function on your calculator and answer the questions about it on this paper:</p><p>1. f(x) = -2(x + 4)2 + 1 a. The graph of the function is concave ______and therefore it has a </p><p>______.</p><p> b. Identify the coordinate of the vertex </p><p> c. Since the function is no longer at the origin, describe in words its location in </p><p> terms of the origin. Be specific. </p><p> d. Simplify the equation so that it is in the form f(x) = ax2 + bx + c. Show your</p><p> steps below.</p><p>2. f(x) = 3(x - 1)2 – 4</p><p> a. The graph of the function is concave ______and therefore it</p><p> has a ______.</p><p> b. Identify the coordinate of the vertex </p><p> c. Since the function is no longer at the origin, describe in words its location in </p><p> terms of the origin. Be specific. </p><p> d. Simplify the equation so that it is in the form f(x) = ax2 + bx + c. Show your</p><p> steps below.</p><p>SATEC/Algebra II/Quadratic F’ns/Parameter Changes/ 0e56e1158b119d4c41b798cac9ed7034.doc/Rev. 07-01 Page 5 of 9 e.</p><p>3. f(x) = 2(x - 3)2 - 5 a. The graph of the function is concave ______and therefore it </p><p> has a ______</p><p> b. Identify the coordinates of the vertex: </p><p> c. Since the function is no longer at the origin, describe in words its location in </p><p> terms of the origin. Be specific. </p><p> d. Simplify the equation so that it is in the form f(x) = ax2 + bx + c. Show your</p><p> steps below.</p><p>4. f(x) = 5(x - 3)2 – 2</p><p> a. The graph of the function is concave ______and therefore it</p><p> has a ______.</p><p> b. Identify the coordinates of the vertex: </p><p> c. Since the function is no longer at the origin, describe in words its location in </p><p> terms of the origin. Be specific. </p><p>SATEC/Algebra II/Quadratic F’ns/Parameter Changes/ 0e56e1158b119d4c41b798cac9ed7034.doc/Rev. 07-01 Page 6 of 9 d. Simplify the equation so that it is in the form f(x) = ax2 + bx + c. Show </p><p> your steps below.</p><p>SATEC/Algebra II/Quadratic F’ns/Parameter Changes/ 0e56e1158b119d4c41b798cac9ed7034.doc/Rev. 07-01 Page 7 of 9 5. f(x) = (1/2)(x - 2)2 – 5 a. The graph of the function is concave ______and therefore it</p><p> has a ______.</p><p> b. Identify the coordinates of the vertex: </p><p> c. Since the function is no longer at the origin, describe in words its location in </p><p> terms of the origin. Be specific. </p><p> d. Simplify the equation so that it is in the form f(x) = ax2 + bx + c. Show </p><p> your steps below.</p><p>6. f(x) = -0.4(x + 3)2 – 1</p><p> a. The graph of the function is concave ______and therefore it</p><p> has a ______.</p><p> b. Identify the coordinates of the vertex: </p><p> c. Since the function is no longer at the origin, describe in words its location in </p><p> terms of the origin. Be specific. </p><p>SATEC/Algebra II/Quadratic F’ns/Parameter Changes/ 0e56e1158b119d4c41b798cac9ed7034.doc/Rev. 07-01 Page 8 of 9 d. Simplify the equation so that it is in the form f(x) = ax2 + bx + c. Show your steps below.</p><p>SATEC/Algebra II/Quadratic F’ns/Parameter Changes/ 0e56e1158b119d4c41b798cac9ed7034.doc/Rev. 07-01 Page 9 of 9</p>