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.
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?
• Andre, Juana, Kevin and Emiko go to a soccer
day at the L.A. Galaxy’s 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.
• 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.
• 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.
• After Kevin takes his kick, the coach gives him
a printout of the path of the ball:
• Finally Emiko takes her kick but the computer has a
problem and can only give her a partial table of data
points of the ball’s trajectory.
• Emiko’s 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
• 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.
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:
• 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).