Open-ended items are a great way for students to truly demonstrate their understanding of concepts.  The following two examples allow students to share their conceptual understanding of quadratic functions.

 

Example 1

Original:  Find the vertex and x-intercepts of: f(x) = 5x2 -9x - 6

 

Revised:  Write the equation of a quadratic function with a maximum value and no x-intercepts.

 

Example 2

Original:  Find the solutions:  x2 – 7x – 25 = 5

 

Revised:  Write the equation of a quadratic function with

               (a)     only 1 real solution.

               (b)     only 2 real solutions.

               (c)     no real solution.

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