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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)