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
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.

4. Andre goes first and takes a kick starting 12 yards out from 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.

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 ball’s trajectory.
Emiko’s table
Distance
Height

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).