Lesson Goals: (Annot. 04, All)

Share and discuss briefly the following goals to the class and invite students to comment or pitch in other goals they think are relevant to the lesson either in writing or verbal.  Suggestions will remain anonymous.

1. Students will identify the defining characteristics of a quadratic function.

• Distinguish how the characteristics are represented symbolically and graphically

• Recognize patterns and relationships among certain characteristics of the function (for example, deducing the y-intercept by noticing patterns in the roots.)

• Describe the meaning of the vertex, y-intercept, and x-intercept(s) by analyzing the behavior of a quadratic function at and around those points

2. Students investigate the coefficients in symbolic expressions of quadratic functions, and how varying coefficients are reflected in graphs.

3. Students identify significant points on a parabola and how these are reflected in symbolic expressions.

4. Students make connections between graphical and symbolic representations by examining and manipulating the three symbolic forms of a quadratic function in order to predict shape, orientation (opens upward or downward), and location.

               Three forms of quadratic equation:

               polynomial:  y = ax2 + bx + c,
              
vertex:  y = a (x-h)2 + k,
               root:  y = a (x-r1)(x-r2)
 

5.      Students will gain deeper understanding of quadratic functions as they become more aware and motivated to observe and reflect on its application in their environment (Annot 05, All).