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Unit 2 – Non­Linear Equations
Lesson 2 – Quadratic Graphs and Equations

                               Slow­Motion Tennis Ted White 
                               This picture was produced in a dark 
                               room, with a strobe light and a camera 
                               that was capable of taking long exposure 
                               shots (by keeping its shutter open longer). 
                               The parabolic shapes brilliantly 
                               demonstrate the relative time that it takes 
                               for the ball to travel throughout the various 
                               points of the image.   At the very top of 
                               the parabola, the tennis ball images appear 
                               very close together, therefore indicating 
                               that the ball moved at a slower velocity.   
                               Conversely, near the bottom of the 
                               parabolas, the distances between the 
                               images of the ball grow larger, therefore 
                               indicating that the ball moved more space 
                               per time interval as it descended toward 
                               the racket.   This slow­motion tennis 
                               picture helps one more easily visualize the 
                               properties of parabolic motion, as defined 
                               by Earth's gravitational force.   

                               http://science.jburroughs.org/mschober/photo
                               s/photocontest06/photocontest06­
                               Pages/Image12.html




                                                                                2
http://people.rit.edu/andpph/photofile­misc/coin­flip_4509.jpg




                                                                 3
http://people.rit.edu/andpph/photofile­misc/stroboscope­ppball_4980.jpg




                                                                          4
http://commons.wikimedia.org/wiki/File:Bouncing_ball_strobe_edit.jpg




                                                                       5
The equation of a quadratic function is

       y = ax2 + bx + c                   y=ax2 + bx + c

The shape of this function’s graph is a parabola.




                                                           6
Some parabolas have a minimum and some have a 
maximum.
• If a is positive, the parabola opens upward, and the 
parabola has a minimum.
• If a is negative, the parabola opens downward, and the 
parabola has a maximum.




                                                            7
The zeros of a quadratic function are the x­coordinates where the 
   function intercepts the x­axis.

   They are found when y=0.  Parabolas may have 0, 1 or 2 zeros.




0 x­intercepts               1 x­intercept                 2 x­intercepts




                                                                            8
The vertex is the maximum/minimum point of the parabola.

The vertex is the place where the parabola changes direction.

The vertex is identified by x­ and y­coordinates
e.g. (­1.5,­1)




                                                                9
If the vertex is identified by x­ and y­coordinates
e.g. (­1.5,­1), then..

The axis of symmetry is the vertical line through the vertex.  Its equation is x = m where m is the x 
value of the vertex.




                                                                                                         10
11
Investigation of Quadratics

• In groups of 2 or 3, complete Investigation 2




                                                  12

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writing about opinions about Australia the movie
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10 quadratics