Possible solution to DA of Applications of Derivatives

Instead of a multiple choice, numerical response and a written response exam on "Applications of Derivatives", I gave my students an open-ended assessment.

Here is one of my student's work. As you can see, students still can demonstrate knowledge and understanding without shading in "c" on a scantron sheet.

DA with Quadratics

Before, I have assessed Quadratic functions in the traditional sense with worksheets, homework checks and quizzes.  This year I wanted to assess my students' knowledge through an open-ended project and allow for differientated assessment.

Here is the task:

Quadratic Graph Project

1.      Take a digital copy of a picture which has a parabolic shape in it.

2.      Log on to www.prezi.com using the following log on:

***I just created a class log on and password***

3.      Select blank template.

4.      Select insert picture, and import your picture onto the prezi.

5.      Using insert à shapes àlines, draw in two axes.  Neither axis may go through the vertex of the parabola.

6.      Using either the pen tool or the circle tool, create a point on the vertex of the parabola

7.      Label the vertex using points which are appropriate.

a.       Vertex:____________

8.      Label another co-ordinate on the graph.

a.       Point:_____________

9.      Using your vertex and co-ordinate you created, determine the value of a, either as a fraction or a whole number, if your parabola was written in standard form .  Show your work on Prezi.

a.      

10.    Label another 4 points on your graph.  Try to space out the co-ordinates evenly across the parabola.

a.       Point 1:_______

b.      Point 2:_______

c.       Point 3:_______

d.      Point 4:_______

e.       Vertex:_______

11.  We will now have the calculator create the function.

a.       On your calculator, push STAT, then EDIT…

b.      In the first column (L1) input all the x-values, and in the second column (L2) input all the y-values of the points.

c.       Click STAT, then the right arrow  (à) to the CALC menu, then scroll down to QUADREG.

d.      Write down the values your calculator gives you, to the nearest hundredth if necessary.

                                 a:__________

                                 b:__________

                                 c:__________

12.  Inputting your values into general formyour function will be_____________________

13.  Change your general form into standard form, by completing the square.  Show your work in prezi.

a.       Your standard form now is ________________
b.      State the vertex, domain, range, direction of opening, and axis of symmetry from the function above.

14.  Write a couple of sentences explaining any differences from the vertex you stated in part 7, and the vertex in part 13.

15.  Using the equation from Part 9, determine the functions x and y intercepts, if the picture was extended such that it intercepts both axes.  Solve this part by graphing.

a.       x-intercept________

b.      y-intercept________

16.  Using the equation from Part 12, determine the functions x and y intercepts, if the picture was extended such that it intercepts both axes.  Solve this part by the quadratic formula.

a.       x-intercept________

b.      y-intercept________

Here is an example of my student working up to Section 14.