RECOGNIZING THE QUADRATIC FUNCTION
Maximumor
Minimum
AXIS OF SYMMETRY
VERTEX
Y - INTERCEPT
X-INTERCEPTSZEROS
SOLUTIONSROOTS
FACTORS
VERTEX FORM
Y = a(x-h)2 + K
STANDARD FORM
Y = ax2 + bx + c
WORD PROBLEMSubstitute Time in X Height in Y
Y-INTERCEPT MEANVERTEX MEAN
X-INTERCEPT MEANCONTRAINTS
TRANSFORMATIONKnow Parent Function
Horizontal ShiftVertical Shift
Stretch or ShrinkReflection
DERIVING THE QUADRATIC FORMULA
IDENTIFY CHARACTERISTICS OF GRAPHSHAPE
MAXIMUM OR MINIMUMAXIS OF SYMMETRY
VERTEXX-INTERCEPTSY-INTERCEPTS
DOMAIN AND RANGEEND BEHAVIORS
CHANGE STANDARD FORM TO
VERTEX FORM
IDENTIFY THE VERTEX POINT
FROM THE VERTEX FORM
FIND THE SOLUTIONS
FROM VERTEX FORM
CHANGE VERTEX FORM TO STANDARD
FORM
LIST 8 WAYS OF FACTORING
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
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
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)
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)
FACTORING x2+bx+cSome trinomials can be written as
the product of two binomials
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
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
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
3. Check
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
FACTORING
SOLVING
COMPLETING THE SQUARE
QUADRATIC FORMULA
FACTORING
GRAPHING
USING SQUARE ROOTS
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)
