FORMULAS & FACTS I NEED TO KNOW FOR THE REGENTS Flashcards

1
Q

Positive Perfect Square

A

Real, rational, unequal

2 x-intercepts

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2
Q

Positive Nonperfect Square

A

Real, irrational, unequal

2 x-intercepts

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3
Q

Zero

A

Real, rational, equal

1 x-intercept

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4
Q

Negative

A

Imaginary

0 x-intercepts

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5
Q

i^0

A

1

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6
Q

i^1

A

i

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7
Q

i^2

A

-1

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8
Q

i^3

A

-i

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9
Q

Standard Form of an Equation of a Parabola with vertex (h,k)
p= distance from vertex to focus (or vertex to directrix)
USE THIS EQUATION FOR FOCUS/DIRECTRIX PROBLEMS

A

(x-h)^2 = 4p(y-k)

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10
Q

Exponential Growth Model
y= ending amount
a= initial amount
r= rate of change
* percent rate of change (% increase/decrease)= r x 100%
^ To interpret percent rate change, the coefficient of t must be 1

A

y= a(1+r)^t
Growth factor = b= 1 + r
For exponential GROWTH, b> 1

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11
Q

Exponential Decay Model
y= ending amount
a= initial amount
r= rate of change
* percent rate of change (% increase/decrease)= r x 100%
^ To interpret percent rate change, the coefficient of t must be 1

A

y= a(1-r)^t
Decay factor= b= 1-r
For exponential GROWTH, 0<b></b>

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12
Q
CONTINUOUS GROWTH/DECAY 
where y= ending amount 
t= time 
P= initial amount 
r= rate of change
* NOTE: r is positive for continuous growth, r is negative for continuous decay
A

y= Pe^rt

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13
Q
COMPOUNDING "n" TIMES 
where y= ending amount 
t= time 
P= initial amount 
r= rate of change
n= number of times compounded in a year
A

y= a(1+r/n)^nt

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14
Q

“HALF LIFE” FORMULA
y= ending amount
a= initial amount
b= growth/decay factor (ex: b=1/2 for half life, b=2 for doubling, etc.)
t= time (usually in years)
H= “half life” (# of units of time it takes for substance to grow/decay)
* NOTE: This formula can be modified for any type of exponential growth/ decay that grows every # units of time.*

A

y= a(b)^t/H

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15
Q

EXPONENTIAL AND LOGARITHM RULE

Product

A

Exponential
x^m x x^n=x^m+n
Logarithm
Log_bmn=Log_bm + Log_bn

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16
Q

EXPONENTIAL AND LOGARITHM RULE

Quotient

A

Exponential
x^m/x^n=x^m-n
Logarithm
Log_bm/n=Log_bm-Log_bn

17
Q

EXPONENTIAL AND LOGARITHM RULE

Power

A

Exponential
(x^m)^n=x^mn
Logarithm
Log_bm^n=nLog_bm

18
Q

MORE EXPONENT RULES

A

Look to green packet for answers

19
Q

Discriminant

20
Q

Trig ratios

A
SINE 
Opposite over hypotenuse 
COSINE 
Adjacent over hypotenuse
TANGENT 
Opposite over adjacent 
COSECANT
Hypotenuse over opposite
SECANT 
Hypotenuse over adjacent 
COTANGENT
Adjacent over opposite
21
Q

DEGREES TO RADIANS AND RADIANS TO DEGREES

A

DEGREES TO RADIANS
Multiply by pie over 180 degrees
RADIANS TO DEGREES
Multiply by 180 degrees over pie

22
Q

ARC LENGTH OF A CIRCLE

A

S=(phata)(r)

S= arc length
Phata= central angle intercepting the arc, in RADIANS 
r= radius
23
Q

ON A UNIT CIRCLE

A
x= cosine 
y= sine 
(x,y)= (cosine, sine) 
tangent= y over x= sine over cosine 
PYTHAGOREAN TRIG IDENTITY 
sine^2 + cosine^2= 1
24
Q

CAST

A

Quadrant 1- ALL trig functions are POSITIVE
Quadrant 2- SINE IS POSITIVE
Quadrant 3- TANGENT IS POSITIVE
Quadrant 4- COSINE IS POSITIVE

25
FINDING COTERMINAL ANGLES
Add or subtract 360 degrees (can do this as many times as needed)
26
RULES FOR FINDING REFERENCE ANGLES
Quadrant 1- phata Quadrant 2- 180-phata Quadrant 3- phata-180 Quadrant 4- 360- phata
27
SPECIAL ANGLES CHART
Phata(in degrees) 30 degrees 45 degrees 60 degrees Sine 1/2 Square root of 2/2 Square root of 3/2 Cosine Square root of 3/2 Square root of 2/2 1/2 Tangent Square root of 3/3 1 Square root of 3
28
TRIGONOMETRIC GRAPHS
y= Asin(B(x-C)) + D y= Acos(B(x-C)) + D |A|= amplitude (height of the curve from the midline to max or midline to min) B= frequency (# of cycles in 2 pie interval) C= phase shift (horizontal shift) D= midline (vertical shift) Period= 2 pie/B (Period is the length of one complete cycle) Note: B= 2 pie/ period
29
ADDITIONAL TRIG GRAPH INFORMATION
- Formula for Magic # = period/4. This tells you how to mark out your x-axis - to find the maximum value: midline + amplitude - to find the minimum value: midline - amplitude - sine functions start at "origin" (midline when translated) - "OMOMO" - cosine functions start at maximum (minimum when reflected)- "MOMOM"
30
ODD, EVEN, OR NEITHER FUNCTIONS
Odd: symmetric to the origin F(-x)= -F(x) Even: symmetric to the y-axis F(x)= F(-x) Both are unequal if its neither
31
GRAPHING POLYNOMIALS
Zeroes= x-intercepts Zeros of ODD multiplicities CROSS the x-axis, zeros of EVEN multiplicities BOUNCE Odd-degree polynomials have end behavior like x^3, even-degree polynomials have end behavior like x^2
32
AVERAGE RATE OF CHANGE
Average rate of change= find the slope Slope formula= y2-y1/ x2-x1
33
FINDING THE INVERSE
The inverse is a reflection in the line y=x (x,y)- (y,x) To find the inverse algebraically, simply switch the x and y values in the equation and then get the equation in y= form.