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Transcript of wrthomashomeworkhelp.weebly.comwrthomashomeworkhelp.weebly.com/.../4/9/...slide3.docx · Web...
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RECOGNIZING THE QUADRATIC FUNCTION
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Maximumor
Minimum
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AXIS OF SYMMETRY
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VERTEX
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Y - INTERCEPT
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X-INTERCEPTSZEROS
SOLUTIONSROOTS
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FACTORS
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VERTEX FORM
Y = a(x-h)2 + K
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STANDARD FORM
Y = ax2 + bx + c
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WORD PROBLEMSubstitute Time in X Height in Y
Y-INTERCEPT MEANVERTEX MEAN
X-INTERCEPT MEANCONTRAINTS
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TRANSFORMATIONKnow Parent Function
Horizontal ShiftVertical Shift
Stretch or ShrinkReflection
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DERIVING THE QUADRATIC FORMULA
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IDENTIFY CHARACTERISTICS OF GRAPHSHAPE
MAXIMUM OR MINIMUMAXIS OF SYMMETRY
VERTEXX-INTERCEPTSY-INTERCEPTS
DOMAIN AND RANGEEND BEHAVIORS
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CHANGE STANDARD FORM TO
VERTEX FORM
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IDENTIFY THE VERTEX POINT
FROM THE VERTEX FORM
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FIND THE SOLUTIONS
FROM VERTEX FORM
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CHANGE VERTEX FORM TO STANDARD
FORM
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LIST 8 WAYS OF FACTORING
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PERFECT SQUARE TRINOMIALFORMULA FACTORS
a x2+2ab+b2 (a+b)2
a x2−2ab+b2 (a−b)2
x2+4 x+4( x+2 ) (x+2 )
(x+2)2
x2−4 x+4( x−2 ) ( x−2 )
(x−2)2
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DIFFERENCE OF SQUARESFORMULA FACTORS
a2−b2 (a−b ) (a+b )
x2−25( x+5 ) ( x−5 )
Check: x2+5 x−5x−25x2−25
SUM OF CUBES
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FORMULA FACTORS
a3+b3 (a+b )(a2−ab+b2)
8 x3+27(2 x)3+33
(2 x+3 )((2 x)¿¿2+(2 x ) (3 )+(3)2)¿(2 x+3 )(4 x2−6x+9)
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DIFFERENCE OF CUBESFORMULA FACTORS
a3−b3 (a−b )(a2+ab+b2)
x3−125x3−53
( x−5 )(x¿¿2+( x ) (5 )+52)¿( x−5 )(x2+5 x+25)
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FACTORING x2+bx+cSome trinomials can be written as
the product of two binomials
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x2+10x+21x2+3x+7 x+21
(x2+3 x )+(7 x+21)x (x+3 )+7 (x+3)
(x+3)(x+7)
1. Find factors of c that add to make b2. Replace b3. Group4. Factor GCF
FACTORING ax2+bx+c
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Some trinomials can be written as the product of two binomials
2 x2+13 x+62 x2+x+12x+6
(2 x2+x )+(12x+6)x (2 x+1 )+6(2 x+1)
(2 x+1)(x+6)
1. Find factors of ac that add to make b2. Replace b3. Group4. Factor GCF
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FACTORING BY GROUPINGIf a polynomial has four or more terms, group terms then factor
3n3−12n2+2n−8(3n3−12n¿¿2)+(2n−8)¿3n2(n−4 )+2(n−4)
(3n2+2)(n−4)
1. Group terms based on GCF2. Factor GCF
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3. Check
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FACTORING GCFFind the GCF of a polynomial’s
terms then factor it out
4 x5−24 x3+8 x
GCF of all three: 4 x4 x5−24 x3+8 x4 x( x4−6 x2+2)4 x5−24 x3+8 x
1. Find GCF of all terms2. Factor GCF3. Check by Distributing
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FACTORING
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SOLVING
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COMPLETING THE SQUARE
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QUADRATIC FORMULA
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FACTORING
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GRAPHING
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USING SQUARE ROOTS
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FORMULA FACTORS
Perfect Square Trinomial
a x2+2ab+b2 (a+b)2
a x2−2ab+b2 (a−b)2
Difference of Squares
a2−b2 (a−b)(a+b)
Sum of Cubes
a3+b3 (a+b)(a2−ab+b2)
Difference of Cubes
a3−b3 (a−b)(a2+ab+b2)
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