Download Solving Quadratic Equations • Factoring • Square Roots

SolvingQuadraticEquations
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Factoring
SquareRoots
CompletingtheSquare
QuadraticFormula
**SOLVINGBYFACTORING**
Factorthequadraticandsolveforx-intercepts/roots/zeroes/solutions
Zero-ProductProperty:
IfAandBareexpressionsandAB=____,thenA=____orB=____.
If(x+5)(x+2)=0,thenx+5=0orx+2=0.Thatis,
x=__________orx=_________.
Examples:Solvethefollowingbyfactoring
1) 3" # − 20" − 7 = 0 3)2" # + 4" = 6
2" # − 11" = −15
2)" # + 7" = 18
4)16" # = 8"
SolvingQuadraticEquations
**SOLVINGBYSQUAREROOTS**
Whensolvingbysquareroots,thereshouldalwaysbe2answers.Whenyoutakethesquarerootof
avalue,youshouldhave±withyouranswer
2 " + 3 # − 8 = 0
Examples:Solvethefollowingbyusingsquareroots
1) 5" # − 180 = 0
2)3" # = 24
3)2 2" + 1
#
− 4 = 6 4)" # −
0
1
= 0
SolvingQuadraticEquations
**SOLVINGBYCOMPLETINGTHESQUARE**
WhenSOLVINGbycompletingthesquare,youdoNOThaveto“undo”thedivisionattheend
2" # − 5" − 10 = 0
Examples:Solvethefollowingbycompletingthesquare
1) 3" # + 6" − 12 = 0 2)" # − 1 = 2"
**COMPLEXSOLUTIONS**
aka: Whenthequadratic_____________________crossthex-axis
Happenswhenyousquareroota__________________________
−1 =
examples: −36 −25 −20
Solvethefollowingbycompletingthesquare
3" # − 18" = −30
Imaginary Numbers: For any positive b,
− b 2 = b 2 • −1
Rule:
Example 1: Simplify the following:
a.
− 25
c.
− 125x 5
b.
Example 2: Simplify2 −12 ∙ 3 −3.
6 − 12
You Try! Simplify
d.
− 121s 8
− 8 ⋅ − 32
Complex Numbers: What is a complex number? a + bi
The _______________ part is ALWAYS first!
Example 3: Name the real and imaginary part of
7 + 4i
Adding and Subtracting Complex Numbers: Only combine like terms. Double check with your calculator.
a) Simplify (6 − 4i ) + (1 + 3i )
b) Simplify (4 − 6i ) − (3 − 7i )
Let x and y be real numbers. What are the values of x and y?
a) ( x + yi ) − (7 − 3i ) = 12 + 9i
b)
( x + yi ) + (9 − 4i) = −3 − 14i
Multiplying Complex Numbers: Make sure to FOIL. Double check with your calculator.
a) Simplify (6 − 4i )(1 + 3i )
b) Simplify (4 − 6i )(3 − 7i )