Getting Started 
Misconception/Error The student does not understand the relationship between the parameters of a quadratic function and its graph. 
Examples of Student Work at this Level The student describes the graphs as:
 Touching the origin or the xaxis.
 Having a minimum x or yvalue.
 Increasing or decreasing.
 “Overlapping” on the right or left side and/or smaller or bigger than the original.

Questions Eliciting Thinking How would you describe the graph of ? What is its graph called? What is the minimum/maximum point on its graph called?
Will the other functions also graph as parabolas?
How will the locations of the graphs compare to the location of in the coordinate plane?
How will the shapes of the graphs compare to the location of in the coordinate plane? 
Instructional Implications Be sure the student has a basic understanding of the parameters of a quadratic function. Tell the student that a quadratic function can be written in vertex form as and explain the effect of each parameter:
 The parameter a affects the rate of change and the orientation of the parabola (opening either up or down, depending on the sign of a).
 The parameters h and k indicate the direction and the number of units the parabola translates. More specifically, the value of h translates the parabola horizontally h units and k translates the parabola vertically k units.
Have the student make a table of functional values for each of , j(x) = , and k(x) . Ask the student to make a multiplicative comparison of functional values for the same value of x and summarize the comparisons in terms of the rate of change (e.g., function j is increasing twice as fast as function f ). Make clear that (h, k) describes the coordinates of the vertex of the parabola.
Using a graphing utility, ask the student to graph along with a number of other functions of the form varying the values of a, h, and k. Ask the student to compare each graph to the graph f and to describe g in terms of specific transformations of f.
Have the student predict the effect of changing parameters of a quadratic function on its graph and then check the predictions using a graphing calculator or an interactive website such as Math Open Reference: Quadratic Function Explorer (http://www.mathopenref.com/quadvertexexplorer.html).
Consider implementing other MFAS tasks for FBF.2.3. 
Making Progress 
Misconception/Error The student cannot provide a complete description of the transformations of the graphs. 
Examples of Student Work at this Level The student understands that a transformation has been applied to the parabola but is unable to describe the transformation using appropriate terminology. The student describes the transformation:
 By drawing arrows and writing the number of units.
 Of only the vertex.
 In general terms without specifying the number of units translated.
 As the parabola moving up/down and left/right and writing the number of units.

Questions Eliciting Thinking What do your arrows mean? Can you describe the movement of the graph using mathematical terminology?
Did only the vertex get translated? What about the rest of the graph?
Can you be more specific in your description? How many units did the graph translate in each direction? 
Instructional Implications Be sure the student has a basic understanding of the parameters of a quadratic function (i.e., a, h, and k) and how these parameters are related to various transformations of the graph of f(x) = . Review the terminology of transformations (e.g., translations and reflections) and guide the student to compare graphs of quadratic functions by describing one as a translation of the other or as a reflection across an axis. Remind the student that the parameter a affects the rate of change, so differences in “width” can be described in terms of the rate of change. Assist the student in describing transformations in specific terms.
Ask the student to reevaluate and revise the descriptions that he or she originally wrote. Then give the student descriptions of graphs of quadratic functions compared to the graph of (e.g., function h is a vertical translation 6 units up and 2 units left of function f ) and ask the student to write the equation of function h.
Consider implementing other MFAS tasks for FBF.2.3. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student provides a correct description of how each graph compares to the graph of f. The student explains that the graph of:
 is a translation of f down two units and left three units.
 is a translation of f up six units and right four units.
 is a transformation that affects the rate of increase of the graph. The graph of j is increasing twice as fast as the graph of f.
 is a transformation that affects the rate of increase of the graph. The graph of k is increasing half as fast as the graph of f.
 is a reflection of f across the xaxis.

Questions Eliciting Thinking What are the coordinates of the vertex of each of these functions?
Can you write the equation of a translation 10 units down and 4 units to the right of ? 
Instructional Implications Challenge the student to compare the graphs of quadratic functions to a quadratic function other than . For example, ask the student to compare the graph of to the graph of .
Have the student explore transformations of other types of functions (e.g., absolute value) and develop general rules for the effects of parameters on the graphs of functions.
Consider implementing other MFAS tasks for FBF.2.3. 