alg1_complete_the_square.notebook
April 27, 2015
Solve by square root.
(x - 3)2 + 2 = 6
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alg1_complete_the_square.notebook
April 27, 2015
Expand (x - 3)2 first.
Then solve (x - 3)2 + 2 =6 by factoring.
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alg1_complete_the_square.notebook
April 27, 2015
Solve by graphing.
(x - 3)2 + 2 = 6
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alg1_complete_the_square.notebook
April 27, 2015
Solve by the most efficient method.
(x - 10)2 = 100
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alg1_complete_the_square.notebook
April 27, 2015
Goal:
1. Place quadratics in vertex form by
completing the square.
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alg1_complete_the_square.notebook
N9
April 27, 2015
4-27-15 Complete the square
What would we need to add to "complete the square?"
x2 + 6x
+ ______ = (x + 3)2
x2 - 4x
+ ______ = (x - 2)2
x2 - 12x + ______ = (x - 6)2
x2 + 36x + ______ = (x + 18)2
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alg1_complete_the_square.notebook
April 27, 2015
Why do we complete the square?
1. Forces a quadratic to factor, so you can
then solve for x.
2. Allows you to convert from standard
form to vertex form and see
transformations from f(x) = x2.
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alg1_complete_the_square.notebook
April 27, 2015
Steps to complete the square
1. Put quadratic in standard form & set equal to zero.
2. Make sure the value of "a" is 1, if not, factor out a # from just
ax2 & bx.
3. Take 1/2 of "b" and square it. You have just added a # to your
equation, so to keep it balanced, you also have to subtract that #
from the equation.
4. Factor into a binomial squared and solve for x.
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alg1_complete_the_square.notebook
April 27, 2015
1. Place in vertex form f(x) = x2 - 4x +6.
Graph. Identify domain and range.
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alg1_complete_the_square.notebook
April 27, 2015
2. Place g(x) = x2 + 7x - 26 in vertex
form. Graph. Identify domain and range.
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alg1_complete_the_square.notebook
April 27, 2015
3. Identify the vertex, horizontal and
vertical shifts, and opening direction for
t(x) = x2 + 20x + 40.
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alg1_complete_the_square.notebook
April 27, 2015
4. Find the roots of 9x2 = 49.
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alg1_complete_the_square.notebook
April 27, 2015
5. Solve x2 + 10x = -21.
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alg1_complete_the_square.notebook
April 27, 2015
Graph and identify domain and range:
6.
7.
8.
9.
h(x) = -x2 - 2x - 5
p(x) = x2 - 8x + 5
g(x) = 2x2 + 11 - 4x
Solve 2x(x + 1) = 7x - 2
10. Solve 2x2 - x = 6
11. Solve x2 = 5x
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alg1_complete_the_square.notebook
April 27, 2015
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