Multiple%20Representations%20on%20Quadratic%20Functions

1
Multiple Representations on Quadratic Functions

• 9. Compare properties of two functions each
  represented in a different way (algebraically,
  graphically, numerically in tables, or by verbal
  descriptions). For example, given a graph of one
  quadratic function and an algebraic expression
  for another, say which has the larger maximum.

2
Warm up

• How do you find the axis of symmetry of a
  quadratic Equation?
• How do you find the vertex of the quadratic
  equations?
• Is there another method?
• How do you determine the maximum or minimum value?

3

• Andre, Juana, Kevin and Emiko go to a soccer day
  at the L.A. Galaxys training field at the Home
  Depot Center.The coach has a computer and video
  system that can track the height and distance of
  their kicks. All four soccer players are
  practicing upfield kicks, away from the goal.

4

• Andre goes first and takes a kick starting 12
  yards out from goal. His kick reaches a maximum
  height of 17 yards and lands 48 yards from the
  goal.

5

• Juana goes next and the computer gives the
  equation of the path of her kick as
  y x2 14x 24, where y is the height
  of the ball in yards and x is the horizontal
  distance of the ball from the goal line in yards.
  

6

• After Kevin takes his kick, the coach gives him a
  printout of the path of the ball

7

• Finally Emiko takes her kick but the computer has
  a problem and can only give her a partial table
  of data points of the balls trajectory.
• Emikos table
• Distance 10 11 12 13 14 15 16
  17 18 19 20
• Height 0 4.7 8.7 12.2 15 17.2 18.7
  19.7 20 19.7 18.7

8

• The computer is still not working but Andre,
  Juana, Kevin and Emiko want to know who made the
  best kick.
• Help them decide by using what you know to find
  (a) Whose kick went the highest?
• (b) Whose kick went the longest?
• (c) Who has the highest rate of change in the
  first 5 yards.
• Be prepared to explain your answer and support
  your reasoning.

9
Assignment

• Suppose Brett and Andre each throw a baseball
  into the air. The height of Brett's baseball is
  given by where h is in feet and t is in seconds.
  The height of Andre's baseball is given by the
  graph below

10

• Brett claims that his baseball went higher than
  Andre's, and Andre says that his baseball went
  higher.
• a. Who is right?
• b. How long is each baseball airborne?
• Construct a graph of the height of Brett's throw
  as a function of time on the same set of axes as
  the graph of Andre's throw (if not done already),
  and explain how this can confirm your claims to
  parts (a) and (b).