SOLVING QUADRATIC EQUATIONS

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SOLVING QUADRATIC EQUATIONS BY COMPLETING THE
SQUARE
BECAUSE GRAPHING IS SOMETIMES INACCURATE, ALGEBRA
CAN BE USED TO FIND EXACT SOLUTIONS.
ONE OF THOSE ALGEBRAIC METHODS IS COMPLETING THE
SQUARE
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SOLVING QUADRATIC EQUATIONS BY COMPLETING THE
SQUARE
Lets solve x2 10x 18 0
Step 1 Get rid of constant on the left side
x2 10x 18 0
-18 -18
x2 10x -18
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SOLVING QUADRATIC EQUATIONS BY COMPLETING THE
SQUARE
Lets solve x2 10x 18 0
Step 2 Add constant to left side to create PST
Half of middle term, then square it.
Must add it to BOTH sides.
25
25
x2 10x -18
(x 5)2 7
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SOLVING QUADRATIC EQUATIONS BY COMPLETING THE
SQUARE
Lets solve x2 10x 18 0
(x 5)2 7
5
SOLVING QUADRATIC EQUATIONS BY COMPLETING THE
SQUARE
Lets solve x2 10x 18 0
Step 3 Square root of both sides.
(x 5)2 7
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SOLVING QUADRATIC EQUATIONS BY COMPLETING THE
SQUARE
Lets solve x2 10x 18 0
Step 4 Solve left side for x
(x 5)2 7
5 5
7
SOLVING QUADRATIC EQUATIONS BY COMPLETING THE
SQUARE
Try this one x2 6x 3 0
3 3
x2 6x 3
Half of 6, squared
9 9
x2 6x 9 12
(x 3)2 12
-3 -3
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FLASH CARDS
COMPLETE THE SQUARE
36 36
x2 12x _____ 3 _____
9
FLASH CARDS
COMPLETE THE SQUARE
16 16
x2 8x _____ 10 _____
10
FLASH CARDS
COMPLETE THE SQUARE
100 100
x2 20x _____ 1 _____
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SOLVING QUADRATIC EQUATIONS USING THE QUADRATIC
FORMULA
Standard form for quadratic equations is
ax2 bx c 0
and can be solved using the Quadratic Formula
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SOLVING QUADRATIC EQUATIONS USING THE QUADRATIC
FORMULA
Example
3x2 7x 2 0
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THE DISCRIMINANT
In a quadratic formula, the discriminant is the
expression under the racical sign.
What is the discriminant for 4x2 2x 7 0 ?
b2 4ac
22 4(4)(-7)
4 112
116
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THE DISCRIMINANT
The discriminant tells you something about the
roots of the equation.
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FLASH CARDS
In the equation, x2 5x 6 0
a
1
16
FLASH CARDS
In the equation, x2 5x 6 0
b
5
17
FLASH CARDS
In the equation, x2 5x 6 0
c
-6
18
FLASH CARDS
In the equation, x2 5x 6 0
the discriminant
49
19
FLASH CARDS
In the equation, 3x2 6 0
the discriminant
72
20
FLASH CARDS
How many roots if the discriminant is equal to
120
Two real roots
21
FLASH CARDS
How many roots if the discriminant is equal to
0
A double root
22
FLASH CARDS
How many roots if the discriminant is equal to
13
Two real roots
23
FLASH CARDS
How many roots if the discriminant is equal to
-15
No real roots