5-5 Completing the Square (Day 1)
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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
x5 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