Verbal Expressions: 4 less than a number: 4 is less than a number: Sum of 3 and x: Twice the difference of x and 4: x-4 x<4 (x+3) 2(x-4)

Literal Equations    

& Independent Variables: Domain & Independent Variables: All x values (numbers from left to right) Range All y values (numbers from bottom to top)

Exponent Examples (-2a2)(3a5) (-6a7) <add exponents> (3a5)2 (64x4y8z)1/2   (125x-3)1/3 = 1251/3x-3(1/3) = 5x-1 = 5 x

Rate of Change Find the rate of change between Day 6 and Day 9 3 Days Flowers 5 12 6 15 7 14 9 3 Days -6 flowers -6 flowers = -2 flowers 3 days 1 day

Estimate the slope of the following lines: 3 -1/2 -5 0 (y= line) Undefined (x = line)

Linear Equations Slope: Y-intercept: Domain: Range: Next = Now+ 2x – 3y = 6 -3y = -2x + 6 -3 -3 -3 y = 2/3x - 2 Linear Equations Slope: Y-intercept: Domain: Range: Next = Now+ X – intercept: 2/3 -2 All Reals All reals 2/3 S.A. -2 3

Slope Formula of (x1, y1) and (x2, y2) Find the slope of the parallel and perpendicular of the line going through (-2,1) and (4, -3) -3-1 -4 = -2 6 3 4- -2 Parallel: -2/3 Perpendicular: 3/2

Y = 4x + 1 Next = Now+ 4 S.A. 1 Y = 1*3x Next = Now*3 S.A. 1 Next = Now Statements Equation Next = Now Y = 4x + 1 Next = Now+ 4 S.A. 1 Y = 1*3x Next = Now*3 S.A. 1 Y = -6x + 10 Next = Now- 6 S.A. 10 Y =8(1/4)x Next = Now * ¼ S.A. 8 .

Slope of Parallel Lines:  Same slope (5/6 & 5/6) Which equation(s) is parallel to y = 3x + 2? y = 2x + 3 B. y = 3x + 5 C. 2y = 6x + 6 (divide by 2) to get y = 3x + 3

Perpendicular Lines: (-1)*Reciprocal ( 5/6 & -6/5) Which line(s) are perpendicular to y = 3x – 2 A. y = -1/3x + 2 B. y = -3x – 2 C. 12y = -4x + 36 (divide by 12) to get y = -1/3x + 3

Find the slope parallel and perpendicular to 2x – 3y = 6 – 3y = -2x + 6 -3y = -2x + 6 -3 -3 -3 y = 2/3x – 2 Slope parallel: 2/3 Slope perpendicular: -3/2

System of Equations 5( )  10x + 15y = 55 -2( ) -10x + 14y = -26 _______________ 29y = 29 y = 1 2x + 3(1) = 11 2x + 3 = 11 2x = 8 x = 4 System of Equations

Jack is three times as old as Mary. Their combined age is 48. How old is Mary? J = 3M J + M = 48 3M + M = 48 4M = 48 M = 12

% & % Increase/Decrease 7% increase (tax)    (1.07)x 20% decrease (off) (0.80)x = (0.8)x Depreciate (Decrease) 5% (.95)x &Appreciate (Increase) 13.5% (1.135)x

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                            

Meaning of Exponential Equations Explain meaning of P = 20(1.03)t where P is the population (in thousands) and t is the time in years since 2005 Population was 20,000 in 2005 and it grows by 3% Explain meaning of P = 15(.93)t where P is the price (in thousands) and t is the time in years since 2009 Price was 15,000 in 2009 and it depreciates by 7%

Exponentials y = 2(3)x Multiplier: 3 Y-intercept: 2 All Reals Domain: Range: Next = Now X – intercept: 3 2 All Reals y>0 *3 S.A. 2 None

Greatest Common Factor (GCF): Largest integer divides in, smallest of each exponent (Calculator: Math Num GCD (#1,#2) ) Find GCF of 42x2yz4 and 28x5 y3 Factor 25x3 – 5x2 GCF: 5x2 5x2 5x2 5x2(5x – 1) Solution: 14x2 y ____ ____

Quadratics y = -x2 + 3x + 4 Opening: Down Y-intercept: 4 X – intercept: Domain: Range: Down 4 -(x2-3x-4) -(x-4)(x+1) 4 & -1 All reals y<6.25

Find area of the trapezoid (A = ½h(b1 + b2) ½ (6) ( x + 3 + 3x + 5) Simplify (2x – 3)(x + 4) 2x(x + 4) – 3(x+4) 2x2 + 8x – 3x – 12 2x2 + 5x - 12 Simplify (2x – 3)-(x + 4) 2x-3 – x - 4 x - 7 Find area of the trapezoid (A = ½h(b1 + b2) ½ (6) ( x + 3 + 3x + 5) 3(4x + 8) 12x + 24 x + 3 6 3x + 5

Midpoint Formula of (x1, x2) and (y1, y2) Midpoint:  Mx =     My = Find the center of the circle with endpoints of (-2,1) and (4, -3) The midpoint is (-3,4) and an endpoint is (1,2). Find the other endpoint. A M B X 1 -3 Y 2 4 -2+4, 1 + -3 2 2 = (1, -1) -4 -4 -7 So (-7,6) +2 6 +2 M M M

Distance between (3,2) &(-3,6)     -4 6

Error on calculator: If you have an error that you can’t fix immediately then reset your memory by:   2nd    +     7    1 2

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