Algebra 1 Final

Solve Linear systems by graphing

(3,3) x+2y=9 3+6=9 YES. 4x-y=15 12-3=15 no NOT A SOLUTION. *FIND A POINT, PLUG IT IN, IF IT WORKS,, SOLUTION IF NOT ITS NOT A SOLUTION*

Factor Special Products

*MUST BE =0 BEFORE FACTORING* (x+2)(x-2) x2-2x+2x-4 x2-4 Difference of Squares x2-16 (x+4)(x-4) 9y2-25 (3y+5)(3y-5) Solve by factoring x2+16x+64=0 (x+8)(x+8)=0 x=-8

Solve Linear Systems By Adding and Subtracting and Mulitplying

1) Add the equations to eliminate the variable 2)Solve the resulting equation for the variable 3)Substitute in either original equation to find the value of the eliminated variable 2x+3y=11 +-2x+5y=13 8y=24 /8. /8 y=3 2x+3(3)=11 2x+9=11 -9. -9 2x=2 /2 /2 x=1 (1,3) 2x+5y=12 5y=4x+6 -4x.-4x -4x+5y=6 2x+5y=12 +(-4x+5y=6)-1 2x+5y=12 +4x-5y=-6 6x=6 /6. /6 x=1

Solve Linear Systems by Substitution

1) pick a variable by itself 2) substitute that into other equation and solve 3) substitute that answer to get other half Solve the system: *ALWAYS COEFFICIENT OF 1* x-2y=-6 +2y +2y x=-6+2y 4x+6y=4 4(-6+2y)+6y=4 -24+8y+6y=4 +24. +24 8y+6y=28 14y=28 /14. /14 y=2 x=-6+2(2) x=-6+4 x=-2 (2,-2)

solve absolute value inequalities

<---AND >----OR

write equations and inequalities

=-equal to <-less than >-grater than

Solve Compound Inequalities

A compound inequality consists of inequalities joined by AND or OR AND is the intersection OR is the union c<-1 OR x>=0 Translate the verbal phrase All real numbers are less than -1 OR grater than or equal to 4. x<-1 OR x>=4 *ALL ARROWS LEFT=AND* *OR INEQUALITIES DONT OVERLAP*

Multi-step equations

ALWAYS KEEP POSITIVE NUMBERS FIRST -20=-4x-6x -20=-10x -20/-10=-10x/-10 2=x 6=1-2n+5 6=6-2n -6 -6 0=-2n 0/-2 -2n/-2 0=n

Mean Median Mode and Range

Mean-add all numbers and divide by how many numbers there are Median-Order numbers from least to greatest and cross out both sides until one or two numbers are in the middle. if there's two numbers, add them and divide by 2 Mode: what number you see the most Range: subtract the bigger number and smallest number

Exponential Growth and Decay

Exponential Growth Model= y=a(1+r)t a=initial amount r=growth rate t=time period y=11000(1+.069)20 y=41778 Exponential Decay: y=a•bx a=y-intercept and b=multiple to increase/decrease by (look at second semester notes date: 5/1/17 for more!!)

Special Products

Find the product. (x+2)2 (x+2)(x+2) x2+2x+2x+4 x2+4x+4✅

Multiply Monomials

Find the product: 2x3(x3+3x2-2x+5) 2x6+6x5-4x4+10x3 ✅ (x-4)(3x+2) F.O.I.L 3x2+2x-12x-8✅

Graph LINEAR equations

Graph the equation: -2x+y=-3 +2x. +2x y=2x-3 y=2(-2)-3 y=-4-3 y=-7 Graph y=3x-2 with a domain of x<-1 y=3(-2)-2 y=-6-2 y=-8

Plot Points in a Coordinate Plane

II |. I | | ------- III. IV

Solve equations in factored Form

If ab=0 than a=0 or b=0 Solve: (x-4)(x+2)=0 x-4=0. x+2=0 x=4 x=-2

Box and Whisker Plots

Order in least to greatest. find Median. Find median or lower half and upper half graph.

Parallel, Perpendicular, Neither

Parallel-Slopes are the same (m) Perpendicular- slopes are opposite reciprocals m=3/2 m=-2/3 Neither-m=3 m=-1/2

Solve Multi-Step Inequalities

Solve 3x-7<8 Graph your solution +7 +7 3x<15 3x/3<15/3 x<5 ~open circle Solve -0.6(x-5)<15 -0.6x+3<15 -3 -3 -0.6x<12 -0.6/-0.6>12/-0.6 x>20 OPEN

Move x to the left first

Solve 6x-7>2x+17 -2x. -2x 4x-7>17 +7 +7 4x>24 4x/4>24/4 x>6 Solve the inequality if possible 14x+5<7(2x-3) -14x. -14x 5<-21 NO SOLUTION 12x-1>6(2x-1) 12x-1>12x-6 -12x. -12x -1>-6 True. ALL REAL NUMBERS

solve proportions using cross products

Solve the proportions 8/x=6/15 120/6=6x/6 120/6=20 x=20 m/5=m-6/4 4m=5(m-6) 4m=5m-30 -5m -5m -m/-1=-30/-1 m=30

Solve inequalities using multiplications and division

Solve using multiplication x/2>4 •2.>4•2 x>8 *WHEN MULTIPLYING OR DIVIDING YOU FLIP YOUR INEQUALITY SYMBOL x/-5<-25 •-5>-25•-5 x>125 Solve using division: -4x>16 -4x/-4<16•-4 x<-4

rewrite equations and formulas

VARIABLE ALWAYS FIRST Literal equations: solve 2x+5=11 x=11-5/2 x=6/2 x=3 Write a functions notation: 3x+2y=7 -3x. -3x 2y=8-3x/2 /2 y=8/2-3x/2 y=4-3x/2

Zero and Negative Exponents

a-n is the reciprocal of an Write Using Positive Exponents 6-4•64=60=1 (2-2)2=4-4=1/44=1/256 *0 TO A POWER IS UNDEFINED* (2xy-5)3=23x3/y15=8x3/y15

Factor Trinomials

a2+bc+c x2+6x+9 (x+3)(x+3) LAST TERM POSITIVE PARENTHESES HAVE SAME SIGN LAST TERM NEGATIVE PARENTHESIS HAVE DIFFERENT SIGN

Solving Inequalities Using Addition and Subtraction

c-9<3 +9 +9 c<12 OPEN CIRCLE- < > CLOSED- <(with lines under them) > write the variable sentence as an inequality: The sun of 11 and m is GREATER than -23 11+m>-23 -11. -11 m>-34 The difference of n and 15 is less than or equal to 37 n-15<=37 +15 +15 n<=52

represent functions as rules and tables

domain-input range-output no input is paired with more than 1 output input variable-independent variable output variable-dependent variable

evaluate functions

f(x)=mx+b a family of functions is a group of functions with similar characteristics

square roots and comparing real numbers

if b2=a than b is a square root of a. "approximate the square root to the nearest integer" 32~7x4 / \ 25 36 | 6=square root of 32

Quotient Rule

m7/m2= m5 x0=1 Product Rule f6•f5=f11 Power Rule (m3)2=m6 [(-6)2]5=(-6)10

Factor Polynomials Completely

n2+2n-1 (n+1)(n-1) Not Factorable 4x3-44x2+96x 4x(x2-11x+24) 4x(x-3)(x-8) GCF 4x 50h4-2h2 2h2(25h2-1) 2h2(5h+1)(5h-1) GCF 2h2

represent functions as graphs

no line connecting ordered pairs on graph

Real Numbers

rational numbers~3/4 -1/3 irrational numbers-sq. r. •integers -1,14,127 of 2 ••whole numbers-0,17,5

Find Slope and Rate of Change

slope=rise/run=change in y/change in x=m m=y2-y1/x2-x1 m=2-6/-4-2=-4/-6=2/3 SLOPE OF EVERY HORIZONTAL=0 VERTICAL=NO SLOPE

one and two step equations

x+7=4 -7 -7 x=-3 x/2+5=11 -5 -5 x/2=6 2/1•x/2=6•2 x=12

Write and Graph Exponential Growth Functions

y=a•bc a=y-intercept b=base(rate of change) y=2•3x b=3 a=2 (Look in Notebook from Semester 2,date:4/27/17 for more!!)

Graph using intercepts

y=x+6 -x -x y-x=6 0-x=6 -0. -0 x=-6 y-0=6 +0 +0 y=6. (-6,6)

Solve Absolute Value

|x|=7 x=+or -7 |x-3|=8 x-3=8. x-3=-8 x=11. x=-5 3|2x-7|-5=4 +5 +5 3|2x-7|=9 /3. /3 |2x-7|=3 2x-7=3. 2x-7=-3 x=5 x=-2 *NEGATIVE=NOT POSSIBLE*

Add and Subtract Polynomials

Monomial: a single term which does not have variables in the denominator or in the exponent. Also, exponents must be infinite numbers. Degree Ex. 10---0 3x---1 1/2ab2---1+2=3 -1.8m3----3 Polynomial: sum of monomial, or just a monomial Degree: greatest degree of it's terms 2x3+x2-5x+12 degree: 3 leading coefficient: 2 Binomial: Sun of 2 monomial (2 terms) 15+x Trinomial: Sum of 3 monomials (3 terms) -x3+15x+3 Adding Polynomials: (2x3 -5x2+x)+(2x2+x3-1) 2x3-5x2+x +x3+2x2. -1 3x3-3x2+x-1 Subtracting Polynomials: (4n2+5)+-(-2n2+2n-4) 4n2+5 +2n2-2n+4 6n2-2n+9