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Comparison Problem
The population of Clinton is 50,000 but is
growing at 2500 people per year. Oak Valley
has a population of 26,000 but is growing at
4000 people per year. When will both towns
have equal population.
Let x = # of years
Let p = population
Clinton
Oak Valley
p  50, 000  2500x
p  26, 000  4000x
50, 000  2500x  26, 000  4000x
2500x
 2500x
50, 000  26, 000  1500x
26, 000  26,000
24, 000  1500x
in 16 years
16  x
Objective - To solve quadratic equations using the
square root method.
Solve.
x 9
2
x  9
2
x 3
x  3
Two Solutions
Solve each equation below.
2
2
n
 169
x

36
1)
2)
x  36
2
n  169
2
x 6
n  13
x  6
n  13
Solve each equation below.
3) y  7
2
y  7
2
y 7
y 7
4) m  6  7
2
6  6
2
m  13
m2  13
m  13
m   13
Solve each equation below.
5) 3y  20  28
2
20  20
2
3y  48
3
3
2
y  16
y  16
2
y 4
y  4
6) 2x  16  4
2
16  16
2
2x  20
2
x  10
x  10
2
x  10
x   10
Solve each equation below.
2
2
7) 2y  30  16
8) 1  5x  2
30  30
2
2
2
2
2y  14
3  5x
2
2
5 5
3
2
y2  7
x
5
15
x


No Real
3
2
5
x

Solution
5
3 5
x 
 
5  5
Solve each equation below.
2
2
9)  y  1  16
10)  x  3  25
 y  1
2
 16
 x  3
2
 25
y 1  4
x 3 5
y  1  4
1  1
y  1  4
x  3  5
3  3
x  35
1  4 1  4
3 or  5
3 5
35
8 or  2
Height of a Falling Object
Acceleration Due to Gravity  16 ft / sec
h  16t  s
2
h  height of object (in feet)
t  time (in seconds)
s  initial drop height (in feet)
2
If a penny is dropped from the top of the
Empire State Building which is 1453 feet
tall, how long will it take to hit the ground?
h  16t  s
2
0  16t  1453
1453
1453
2
1453  16t
16
16
2
90.8125  t
s  1453 ft.
h  0 ft.
2
t   90.8125  9.5 sec. or  9.5 sec.