X-intercept Roots Zeros Hits ground/water ~=0 Crosses x-axis (~,0) Table Method: y1= equation    y2=0  2nd  Trace 5 MOVE Enter Enter Enter  The x values when y=0 (or y goes from + to -) Graphing Method:

y-intercept Initial Value Start at Equation: Table: Calculator:   The number without a variable y= 3x2 +5x + 3 or y = 6(2)x The y value when x = 0 2nd Trace 1(value) 0 Enter

Exponential Growth (Equation): y=abx or y=a(1 + r)x y=final amount   a=initial amount  b=base   r=rate as a percentage  (4.5%= .045) If b > 1 then it’s increase;  If 0<b<1 then it’s decay                            

Decimals of Depreciate (Decrease) 5% &Appreciate (Increase) 13.5% (1- .05) = .95 (1 + .135) = 1.135                           

% & % Increase/Decrease 50$ shirt with 7% increase (tax) 50$ shirt with 20% decrease (off)  Final = Beginning ( 1 +  r)                                    50(1.07)    $53.50 50(0.8)$40

Linear Growth: Slope of y =3x + 2 Y-intercept of y = 3x + 2 y= mx + b  m=slope (rate of change, change per x)  b=y-intercept (crosses y-axis & initial value) 3 (also rate of change ) 2 (also starting value)

The equation p(x) = .5x + 2 where x is the year since 2000 and p(x) represents the population (in thousands) of Pineboro. What is the slope and what does it represent? What is the y-intercept and what does it represent? .5 thousand; increase in population per year 2 population in 2000

Find rate per mile: $2 per .4 mile Find rate per minute: $3 per 30 seconds Find rate per foot: $12 per 10 feet $2/ .4 = $5 per mile $1.20/.2 = $6 per mile 3/.5 = $6 per minute $12/10 = 1.2 per foot

Write equations of the following: Balloon company charges flat-fee of $10 per delivery and $2 per mile Taxi charges a flat-fee of $3 and $2 per 0.5 mile Car rental charges $20 a day plus 65 cents a mile Car rental charges $50 per day C = 2m + 10 F= 2/.5 m + 3 Or F= 4m + 3 C=0.65m + 20 C = 50

& Coefficient of Correlation Regressions & Coefficient of Correlation Coefficient of correlation: STAT   EDIT   Enter x’s into L1 Enter y’s into L2  STAT   CALC  Choose Linreg or Expregr ENTER Write equation on paper and then type in y=     ~1 Positive      ~ -1 Negative                   Find:   2nd 0 Scroll to DiagnosticON Enter  then do regression 

The number of schools in Turnstown can be represented by the following table: According to the line of best fit, how many schools are predicted for 2014? 10 30 44 50 Year 1960 1970 1990 2004 2010 Schools 20 40 80 108 120 Change 1960 to 0 and the other years (only do on year problems) STAT EDIT Put the numbers in STAT CALC Linregression 3) Write the equation. Y = 2x + 20 4) Type Equation into Y= y = 2x + 20 5) Look at table for x=54 (2014-1960 = 50) 54  128

Exponent Examples 2a2*3a5 (3a5)2 = 2aa 3aaaaa = 6a7 Multiply: Mult. Coefficients, add exponents = (3aaaaa)(3aaaaa)= 9a10 Power: Write it out then perform rule

Exponent Examples Continued: Write out the variables; reduce the coefficients; cancel letters Negative exponents: Switch the location and make positive; 5xo = 5 Zero power makes exponent disappear

Write it out twice Move negative exponents Write out exponents; remove Zero exponent Combine exponents Subtract exponents

Dividing by a monomial Simplify Divide each by the bottom 6x3 Divide each by 6x3 6x3 6x3 6x3 Simplify

Greatest Common Factor (GCF): 42x2yz4 and 28x5 y3 Largest integer that goes into each coefficient Smallest of each exponent 14x2 y Calculator (for coefficient) Math Num GCD (#1,#2) z

Least Common Multiple (LCM): Example: 10x2 yz4 and 15x5 y3 Smallest integer they go into, largest of each exponent LCM: 30x5y3z4

Slope of Parallel Lines: What is the slope of the line parallel to y = 3x + 2? 3x + 2y = 8  Same slope (5/6 & 5/6) 3 2y = -3x + 8 y = -3/2x + 8/2 so -3/2

Slope of Perpendicular Lines: What is the slope of the line perpendicular to y = 3x + 2? What is the slope of the line perpendicular to 3x + 2y = 8  Negative Reciprocal slope (5/6 & -6/5) -1/3 2y = -3x + 8 y = -3/2x + 8/2 so 2/3

Direct Variation: (Set up Proportion then solve) Y varies directly as x. y is 8 when x is 3. Find x when y is 40 Y = Y X X Write proportion 8 = 40 3 X Substitute in Cross multiply 8x = 3(40) Solve by dividing x = 120/8 = 15

The number of dolls made varies directly as the number of hours worked The number of dolls made varies directly as the number of hours worked. 100 dolls are made in 25 hours. Find how many dolls are made in 75 hours dolls = dolls hours hours Write proportion 100 = d 25 75 Substitute in Cross multiply 25x = 75(100) Solve by dividing x = 7500/25 = 300

Systems of Equations 2x – y = 10 Find x + y x = y + 4 2x – 1y = 10 Put in matrix ready mode with x’s and y’s together 2nd x-1   1 ENTER 2 X 3 [ 2 -1 10 ] [ 1 -1 4 ] Put into matrix Solve with matrix 2nd MODE 2nd x-1  Scroll to RREF 2nd x-1 1 ENTER You get [ 1 0 6 ] so x = 6 and y = 2 so x + y = 8 [ 0 1 2 ]

Midpoint of (x1, x2) and (y1, y2) Midpoint:  Mx =     My = Or Graph to find Midpoint Midpoint is ½ way Find midpoint of (3,2) and (-1,5) (1, 3.5)

Mary’s house is (3, 1) and is the exactly halfway between Jack’s house (-1,3) and Gary’s house? Find the coordinates of Gary’s house. Jack’s House Down 2 Midpoint Right 4 Down 2 Gary’s House (5, -1) Right 4

What does An+1=2An + 3 mean? Next number = 2 * (now number) + 3

Describe the change in butterflies Increases by 12% every day The number of butterflies, of a particular day, is related to the previous day’s number of butterflies, Bn by the function Bn+1 = 1.12Bn. Describe the change in butterflies Increases by 12% every day (112% - 100% = 12%) B)Find the number of butterflies on the 4th day if there was 50 butterflies on the first day Day 1: 50 Day 2: 50(1.12) = 56 Day 3: 56(1.12) = 62.7 Day 4: 62.7(1.12) = 70.24 butterflies

Factor trick with Calculator (only for multiple choice) Use if given area or “Which is a factor? 37 STO X ENTER Store 37 as x (Problem) / (Answer A) If no decimal then it could be a factor (Problem)/(Answer B) (Problem)/(Answer C) (Problem)/(Answer D) Example: Area is 10x2 – x – 2. Which could be a length? A) 5x – 2 B) 2x + 1 C) 10x – 3 D) 2x - 1 37 STO X ENTER Store 37 as x (10x2 – x – 2 ) / (5x – 2) Decimal so not a factor (10x2 – x – 2)/(2x + 1) Decimal so not a factor (10x2 – x – 2)/(10x – 3) Decimal so not a factor (10x2 – x – 2)/(2x – 1) NOT A DECIMAL so it’s the answer!

& Independent Variables: Domain & Independent Variables: All x values (numbers from left to right) Domain of {(2,3),(5,6),(1,8)} Domain of y = x2 + 3x {1,2,5} All reals

& Dependent Variables: Range & Dependent Variables: All y values (numbers from down to up) Range of {(2,3),(5,6),(1,8)} Range of y = x2 + 6x {3,6,8} y> -9 (-3,-9)

Error on calculator: If you have an error that you can’t fix immediately then reset your memory by:   2nd    +     7    1 2 If calculator keeps saying 2nd Curve when finding intersection then make sure you have y2 = 0

Slope of (x1, x2)  and (y1, y2)  m=

Distance between (x1,x2) &(y1,y2)     don’t forget to close the parenthesis

Pythagorean Theorem  Pythagorean Theorem:   a2 + b2 = c2       c a b

Area of rectangle and triangle: Rectangle A=lw Triangle A = ½ bh

Area &Circumference of Circle: Area: A= (3.14) r2 Circumference=2(3.14)r  or  (3.14)d

Other Reminders: 4 less than a number: 4 is less than a number: x-4 Sum of 3 and x: Twice the difference of x and 4: There are twice as many cats as dogs Quadrants: x-4 x<4 (x+3) 2(x-4) c = 2d  II           I      III           IV