Notes 5.8B Quadratic Applications - Kenston School District

5-8B: Quadratic Applications
Objective:
• To solve real­world problems using quadratic function information
(vertex, y­intercept, and x­intercept).
Directions:
• Read each question and formulate a plan of your own.
• Discuss the plan with the person sitting next to you.
• Mrs. Fruchter will ask for volunteers to explain each problem.
Problem #1:
The height of a ball thrown upward is shown
as a function of time on the given graph.
a. Estimate the initial
height of the ball.
b. Approximately when
did the ball reach its
maximum height?
c. What was the
maximum height?
_______
_______
_______
d. When was the ball
8 meters high? _______
_______

Problem #2:
Refer to the diagram given.
Calculate the area of each region.
(Be sure to write the answers in standard form.)
a. Area of the shaded rectangle:
Problem #3:
Suppose a park district plans to build a rectangular playground
that is 80 meters by 60 meters with a walkway that is w meters
wide around it.
a. Label the diagram to
represent this situation:
________________________________
b. Area of the larger rectangle:
________________________________
c. Area of the un­shaded region:
b. Write an expression in standard form for the total area of the
playground and the walkway.
________________________________
________________________________
c. Find the total area if w = 3.

Quadratic Application Notes:
Vertical Motion Formulas
When units are in feet:
When units are in meters:
h = t =
v = c =
EX #2:
Suppose a water balloon is dropped from
the top of a 79 foot tall tree.
a. Write an equation that describes the relationship
between the height of the ball above the ground
(h) and the time (t) in seconds.
b. Use the table below and the
grid at the right to graph your
equation from part a.
EX #1:
Suppose a ball is thrown upward from a height of 5 feet with an
initial velocity of 30 ft/sec.
a. Write an equation relating the time (t) in seconds and the
height (h) of the ball in feet.
b. Find the height of the ball after 1.5 seconds.
c. Using your graph, estimate how long it would take the ball to reach
the ground. Explain your reasoning.

EX #4:
Michael threw a water balloon upward at a
speed of 10 m/sec while standing on the roof
of a building 12 meters high.
a. Write an equation relating the time in seconds and the height of
the balloon in meters.
EX #3:
On the graph, the height (ft) of a baseball hit upward is
shown as a function of time (sec).
a. What was the initial height
of the ball?
b. What was the height of the balloon after 2 seconds?
c. Assume that the balloon did not land on the roof,
about how long did it take for the balloon to reach the ground?
b. When did the ball reach its
maximum height?
c. What was the maximum
height?
d. When was the ball 30 ft
in the air?
e. When did the ball hit the ground?

EX #5:
A model rocket was launched straight up with an initial velocity
of 75 m/sec. The launch pad was 2.3 m off the ground.
a. Write an equation relating the
time (t) and the height (h).
EX #6:
A square room and a rectangular room require the same amount of
carpeting. The length of the rectangular room is 8 feet less than twice
the side of the square room. The width of the rectangular room is 3
feet less than the square's side.
b. When will the rocket reach a height
of 100 m? (Use your calculator.)
a. Let x represent the length of the side of the square.
Write expressions for the dimensions of the rectangle:
c. When will the rocket hit the ground?
length = ____________
width = ____________
b. Write an equation that represents the relationship between the
square and the rectangle. Solve for x.
c. Find the dimensions of both figures.
square = ____________
rectangle = ____________

EX #7:
Sherman hit a fastball thrown by Austin.
Let x be the distance on the ground in feet
of the ball from home plate and h(x) be the
height in feet of the ball at that distance.
Suppose the path of the ball is described
by the function:
a. Define your variables:
x = ____________
y = ____________
b. How far from the plate, along the ground, was the ball when it was
again at the same height at which Sherman hit it?
c. How far from the plate, along the ground, was the ball when it was
100 feet high?
d. The fence is 405 feet from home plate, and it is 12 feet high.
Did the ball go over the fence? __________ Prove it.