Name_______________________________________________ Date __________ Per _______
Quadratic Applications pt 1
1. The length of a rectangle is x ft and the width is x+6 ft. The area is 91 ft². What are the
dimensions of the rectangle?
2. Find the length and width of the rectangle below:
15 in²
x
x+3
3. The length of a rectangle is 4 meters more than the width. The area is 30 m². Find the length.
4. The length of a rectangular mural is 2 feet more than three times the height. The area is 165 ft².
Find the height of the mural.
5. Find the value of x below.
x
20 cm²
A. If the length of the rectangle is 4,
what is the width?
B. What is the vertex?
What does this point represent?
D. What is the domain? Range?
0
5
C. What are the x-intercepts?
Area of rectangle
6. Use the graph to answer the questions.
10 15 20 25 30 35 40 45 50
x+2
0
2
4
6
8
10 12 14 16 18 20
Length of the rectangle
7. A 7 by 10 in mirror was put in a frame and hung on the wall. The mirror and frame cover an
area of 130 in². How wide is the frame?
8. Suppose you are building an aquarium with a volume of 2880 in³. the aquarium will be 12 in.
high. The base will be a rectangle with the length 4 in. more than twice the width. Find the
dimensions of the base.
Name_______________________________________________ Date __________ Per _______
Quadratic Applications pt 2
Vertical motion formula:
h   16 t  vt  s
2
1. The formula h   16 t 2  45 t  9 gives a ball’s height h in feet at time, t, in seconds. What is the
starting height of the ball? _______. What is the velocity? ______. How many seconds pass
before the ball lands on the ground?
2. A carnival game involves trying to ring a bell with a ball by hitting a lever that propels the ball
into the air. The height of the ball is modeled by the equation h   16 t 2  39 t . If the bell is 25 ft.
above the ground, will you hit tbe ball?
(what is the starting height?____)
(how fast are you hitting the ball? ____)
3. You launch a model rocket with an upward starting velocity of 160 ft/s. When will the rocket hit
the ground? (use the vertical motion formula)
What is the starting height? _____
What is the velocity? _____
What is the equation? ________________
5. Your friend is standing on a balcony which is 38 ft high. You throw a ball up to him with a
velocity of 48 ft/s. The ball is 6 ft. high when it leaves your hand. After how many seconds will
your friend have a chance to catch the ball? (use the vertical motion formula)
Formula: ________________________
6. The height of a ball is shown in the table:
What is the starting height of the ball?
What is the maximum height of the ball. ________
Approximately when will the ball reach 30 feet? _________
Will the ball ever reach 50 ft? ____________
Approximately when will the ball hit the ground? ______________
T (Time)
H (height)
0
3.5
0.5
24.5
1
37.5
1.5
42.5
2
37.5
2.5
24.5
3
3.5
7. Suppose you throw a ball into the air and the height is given by the formula: h   16 t 2  29 t  6
What is the height of the ball after 1.5 seconds? __________ Will the ball ever reach 30 ft?
8. A kid throws the ball in the air from a height of 3 ft with a velocity of 10 ft/s. How long will the
ball be in the air if no one catches it? (use the vertical motion formula: ___________________)
Name _________________________________________ Date_________ Per _______
More Quadratic applications pt1
1. The length of a photograph is 1 cm less than twice the width. The area is 91 cm². Find the
length and width.
2. The dimensions of a rectangular flower garden were 8 m by 15 m. Each dimension what
increased by the same amount. The garden then had an increased area of 198 m².
New length (in terms of x) ________
New width (in terms of x) _________
x = _______
New length _________
New width _________
3. Hugh Betcha launched a rocket with a speed of 88 ft/s. After how many seconds will the rocket
be 40 feet high? (use the vertical motion formula) What is the starting height? _____
Formula ______________
4. The US populations P in millions where t is the number of years after 1900 is estimated by the
equation P  0 . 0089 t 2  1 . 1149 t  78 . 4491 Estimate the population in the year you graduate from
high school. __________________ Estimate the population in 2025. _______________
Name _________________________________________ Date_________ Per _______
More Quadratic applications pt 2
1. The height of a triangle is x and the base is x+6. If the area is 50 cm² what are the actual
dimensions?
2. A football player kicks the ball with an initial upward velocity of 38.4 ft/s from a starting height of
3.5 ft. Use the vertical motion formula to determine how long the ball will be in the air.
3. A diver is standing on a platform 24 ft above the pool. He jumps from the platform with an initial
upward velocity of 8 ft/s. Use the vertical motion formula to determine when he will hit the water.
4. You are building a storage box which needs to have a volume of 4368 ft³. The length of the box
is 24 in. You want the height to be 1 inch more than its width. Find the height and width of the box.