Getting Started 
Misconception/Error The student is unable to find key features of the graph and cannot graph the function correctly. 
Examples of Student Work at this Level The student:
 Is unable to graph the function.
 Attempts to make a table of values and only partially graphs the function.
 Incorrectly divides all terms on the right side of the equation by 16 and graphs the function .
 Graphs the vertex at the yintercept.
 Attempts to find the vertex and then sketches an unrelated graph.

Questions Eliciting Thinking What happens when a rocket is launched? Does it go up at first or immediately begin descending?
What do the variables in the equation represent?
What type of function is this? What will its graph look like? What are some key points to find in order to graph this function?
Does the graph open upward or downward? How do you know?
What is the vertex of your graph?
What is the yintercept of the graph?
What are the xintercepts of the graph?
Can you create a table of values for this function? 
Instructional Implications Review the standard form of a quadratic function, , and explain that the graph of a quadratic function is a parabola. Assist the student in understanding how to identify a quadratic function from its equation. Provide an opportunity for the student to explore the graphs of a variety of quadratic functions by using a graphing calculator or other graphing utility. In each case, ask the student to identify any x and yintercepts, the orientation of the parabola, the coordinates of the vertex, and state whether the vertex is a maximum or minimum.
Provide instruction on graphing quadratic functions. Guide the student to find the vertex and any intercepts along with any additional points needed to sketch the graph. Be sure the student understands to select xcoordinates of points on either side of the vertex and then use the equation to find the associated ycoordinates. Remind the student of the symmetry of the graph. Encourage the student to use symmetry to assist in locating additional points. For example, if the vertex is at (1, 4) and the yintercept is at (0, 3), then the point symmetric to the yintercept about the line of symmetry is (2, 3).
Provide additional opportunities to graph quadratic functions and describe features of their graphs. 
Moving Forward 
Misconception/Error The student does not completely label or scale the axes or does not scale the axes appropriately. 
Examples of Student Work at this Level The student:
 Does not label or scale either the x or yaxis.
 Does not use the same scale throughout the entire axis.
 Uses a scale too small or too large.

Questions Eliciting Thinking What are you graphing on the xaxis? What is the largest value of time?
What are you graphing on the yaxis? What is the largest value of height?
What scale are you using for the time axis? For the height axis?
Where is the vertex? What is a reasonable scale to choose for the yaxis? 
Instructional Implications Guide the student to consider key features of the graph (e.g., intercepts and vertex) and the units of the independent and dependent variable when determining how to scale the axes. Discuss the importance of using appropriate labels and scales on the axes when graphing. Encourage the student to revise the scaling on his or her graph and regraph the function. Remind the student that the two axes can be scaled differently, as long as the same scaling is used throughout each axis. 
Almost There 
Misconception/Error The student graphs the function but extends it beyond a reasonable domain. 
Examples of Student Work at this Level The student graphs the function correctly but shows it extending through second, third, and fourth quadrants which includes values outside of the domain of the function given its context.

Questions Eliciting Thinking Look at the second quadrant of your graph. What do these values mean in the context of this situation? Are these values of t reasonable?
Look at the fourth quadrant of your graph. What do these values mean in the context of this situation? Are these values of t reasonable? 
Instructional Implications Guide the student to consider the context of the function in determining a reasonable domain. Encourage the student to evaluate the graph as a model of the height of the rocket over time.
Have the student examine other functions and their graphs given in the context of real world problems and ask the student to describe reasonable domains. 
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 labels the xaxis â€śTime (in seconds)â€ť and scales it by increments of one. The student labels the yaxis â€śHeight (in feet)â€ť and scales it appropriately for the situation (e.g., the student scales the yaxis by increments of 30, 32, or 40).

Questions Eliciting Thinking How did you choose the scale for each axis?
What is the total flight time of the rocket?
Why did you graph this function only in the first quadrant?
How would you explain to another student why your graph is restricted to the first quadrant? 
Instructional Implications Provide additional practice graphing nonlinear functions that describe the relationship between two quantities. Ask the student to consider an appropriate domain given the context. Challenge the student to interpret key features of the graph in the context of the problem. 