Download Cheat Sheet for College Algebra I | MATH 112 and more Study notes Algebra in PDF only on Docsity! Scatterplot
on
the
Calculator:
!. #ress the STAT *utton 2. Choose $%it ) 0. Clear the list you 5ant to use 4. 7nter the 8ata 9. #ress *+, then STAT -./T :. Choose the #lot you 5ish to turn on ;. Turn the plot on an8 make sure the @list an8 Alist are using the CorreCt list D. #ress 0//M E. Choose EFGoomStat Regression
on
the
Calculator:
!. Make a sCatterplot of the 8ata an8 8etermine if the 8ata is linear, Lua8ratiC or neither. 2. #ress the STAT *utton an8 Choose CA.C 0. Choose either 44.in6eg(a;<=) or ?4@ua%6eg 4. 7nter your list that you use8 an8 5hiCh yC you 5ant your eLuation in 9. Aou line shoul8 *e in the form .in6eg(a;<=) ;list, ylist, yG Formulas:
• Percent Change = ! B"A A #100 . • The slope of a line ! m = y2"y1 x2"x1 . • The point-slope form of the equation of a line is given by ! y = m x " x1( ) + y1 • The slope-intercept form of the equation of a line is given by ! y = mx + b • The vertex form of a quadratic equation is ! f x( ) = a x " h( ) 2 + k . • The vertex of the graph of ! f x( ) = ax2 + bx + c with a ≠ 0 is the point ! "b 2a , f "b 2a( )( ) . • The solutions to the quadratic equation ! ax 2 + bx + c = 0, where a ≠ 0, are given by ! x = "b± b 2"4ac 2a . Absolute
Value
Equations:
• Let k be a positive number. Then ! ax + b = k is equivalent to ! ax + b = ±k . Absolute
Value
Inequalities:
• If ! ax + b < c (5here ! c > 0), then you Can re5rite the ineLuality in one of three 5ays. ! "c < ax + b < c ! ax + b < c and ax + b > "c ! ax + b < c and " ax + b( ) < c • If ! ax + b > c(5here ! c > 0), then you Can re5rite the ineLuality in one of t5o 5ays. ! ax + b > c or ax + b < "c ! ax + b > c or " ax + b( ) > c Types
of
functions:
• Linear function: ! f x( ) = ax + b , where a and b are constants • Constant function: ! f x( ) = b, where b is a constant • Quadratic function: ! f x( ) = ax2 + bx + c , where a, b and c are constants and a ≠ 0 Properties
of
Rational
Exponents
and
Radical
Expressions:
• ! a 1 n = an • ! a m n = am n = an( ) m • ! a "m n = 1 a m n = 1 a ( ) m n • ! a n " bn = a " bn • ! a b n = a n b n • ! ap " aq = ap+q • ! a" p = 1 ap • ! 1 a"p = ap • ! a b( ) " p = b a( ) p • ! ap aq = ap"q • ! ap( ) q = apq • ! ab( ) p = apbp • ! a b( ) p = a p b p Steps
for
Factoring:
1. Factor out all common factors 2. Count the number of terms • 2 terms ! a 2 " b 2 = a " b( ) a + b( ) • Doesn’t factor otherwise • 3 terms – Factor using the ac method • Find 2 numbers m and n such that ! m " n = a " c and ! m + n = b. • Rewrite the trinomial as ! ax 2 + mx + nx + c . • Use grouping to factor this expression as two binomials. • 4 terms – Factor by grouping. 3. Check to see if any of the factors factor further.
