Math Analysis Honors – Worksheet 15
Quadratics – Vertical Motion
Never confuse motion with action. – Ben Franklin
You may use your calculator for all problems.
1
A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight highway. If the
farmer does not fence the side along the highway, what is the largest area that can be enclosed?
2
As a promotion for the Los Angeles Angels of Anaheim, a competition is held to see who can throw a baseball the
highest from the front row of the upper level of seats, 84 feet above field level. The winner throws the ball what an
initial velocity of 92 ft/sec and it lands on the infield grass. The height of the ball is given by
h t   16t 2  92t  83 , where h is measured in feet and t is measured in seconds.
(a) Find the maximum height of the ball.
(b) How much time is the ball in the air total?
3
The Segerstrom High School baseball team uses a baseball throwing machine to help train its players to catch high
pop-ups. It throws the baseball straight up with an initial velocity of 48 ft/sec from a height of 3.5 ft. The height of
the baseball is given by h t   16t 2  48t  3.5 , where h is measured in feet and t is measured in seconds.
(a) How long does it take for the ball to reach its maximum height?
(b) What is the maximum height of the ball?
(c) How long is the ball in the air total?
4
A the Bakersville Fourth of July celebration, fireworks are shot by remote control into the air from a pit that is 10
feet below the earth’s surface. An aerial bomb is launched with an initial velocity of 80 ft/sec and its height is
determined by h t   16t 2  80t 10 ,where h is measured in feet and t is measured in seconds.
(a) How long does it take for the bomb to reach its maximum height?
(b) What is the maximum height of the bomb?
5
Convert f x   2x 2 10x  25 to vertex form. Identify the vertex and axis of symmetry.
6
Accurately Graph f x   2x 2  6x 10 . Identify the vertex and axis of symmetry.