Download Section 5.8

5.8 Applications of Quadratic
Equations
Steps (reviews)
• Read and underline important words and
numbers
• Assign variables
• Create equation and solve equation
• Check
• State answer
Problem with Geometric Figures
1) The length of a hall is five times the width. The
area of the floor is 45m2. Find the length and
width of the hall.
• 1) The length of a hall is five times the width. The area
of the floor is 45m2. Find the length and width of the hall.
5w
w
• Equation:
w (5w) = 45
5w2 = 45
w2 = 9
w2 – 9 = 0
(w-3)(w+3) = 0
w = 3 or w = -3
THEREFORE: The width is 3m
and the length is 5(3) = 15m
Impossible to have negative width
so discard this answer
Problem with consecutive numbers
2) The product of the smallest and largest of
three consecutive odd integers is 16 more
than the middle integer. Find the
numbers.
2)
The product of the smallest and largest of three
consecutive odd integers is 16 more than the middle
integer. Find the numbers.
Let x, x+2, x+4 are three consecutive odd integers
Equation:
x (x+4) = (x+2) + 16
x2 + 4x = x + 2 + 16
x2 + 4x = x + 18
x2 + 4x – x – 18 = 0
x2 + 3x – 18
=0
Therefore, the
(x + 6) (x -3)
=0
numbers are 3, 5, 7
x = -6 or x = 3
-6 is an even number so
discard this answer
4) If an object is propelled upward from ground level with
an initial velocity of 64 ft per sec, its height h in feel t
seconds later is h = -16 t2 + 64t
a) After how many seconds is the height 48ft
b) After how many seconds does the object hit the
ground?
48 = -16t2 + 64t
-3 = t2 – 4t (divide both sides by -16)
t2 – 4t + 3 = 0
(t- 3) (t-1) = 0
t = 3 or t = 1
Therefore, the height is 48 ft after 1 second or after 3
seconds
a)
b) 0 = -16t2 + 64t
0 = t2 – 4t (divide both sides by -16)
0 = t (t – 4)
t = 0 or t = 4
Therefore, the object hits the ground after 4 seconds.
Pythagorean Formula
Hypotenuse c
Leg a
Leg b
a2 + b2 = c2