Transcript 5-5 Completing the Square (Day 1)

5-5: Completing the
Square
Objective:
Solve quadratic equations by
completing the square. Use completing
the square to write quadratic functions
in the vertex form.
Completing the square:
To complete the square for the
we add  b  2
expression
2
x  bx
 
2
Consequently:
2
b
b 
x  bx      x  
2
2 
2
2
Example 1: Find the value of c that
2
makes
a perfect square
x  7 x  c trinomial.
49
 b   7 
c    
4
2  2 
2
2
49
 x  7x 
Prefect square trinomial
4
2
7

x 
2

2
Square of a binomial
Example 2: Solve x 2  10 x  3  0
x  10 x  3  0 Given
2
x  10 x  3
2

1
2
10   5   5   25
2
Add 25 to both sides.
Solution
x  10 x  25  3  25
2
x  10 x  25  28
2
 x  5
2
 28
x  5   28
x5   4 7
x  5  2 7
x  5  2 7
If the leading coefficient of a
quadratic equation is not 1, you
should divide each side of the
equation by the leading coefficient.
Example 3: Solve
3x  6 x  12  0
2
3 x  6 x  12  0 Given
1
1
2
3 x  6 x  12   0 

3
3
2
x  2x  4  0
2
x  2 x  4 Subtract 4 from both sides.
2

1
2
 2   1   1  1
2
x  2 x  1  4  1
2
 x  1
2
 3
x  1   3
x  1  1 3
x  1 i 3
Homework
Page 286
#24 – 28 even,
#32 – 44 EOE,
#55-61 Odd
Example 4
On dry asphalt the distance d (in feet) needed for
a car to stop is given by:
2
d  0.05s  1.1s
Where s is the car’s speed (in miles per hour).
What is speed limit should be posted on a road
where drivers round a corner and have 80 feet to
stop?
Solution.
d  0.05s  1.1s
2
80  0.05s  1.1s
2
1600  s  22 s
2

1
2
22   11  11  121
2
1600  121  s  22 s  121
2
1721   s  11
2
 1721  s  11
11  1721  s
11  41  s
30  s