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algebra 2 > 2nd semester > Flashcards

2nd semester Flashcards

0
Q

Vertical equation of a parabola

A

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

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1
Q

Vertex of a parabola

A

(h,k)

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2
Q

Horizontal equation of a parabola

A

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

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3
Q

Focus of a vertical parabola

A

(h, k+p)

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4
Q

Horizontal parabola focus

A

(h+p, k)

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5
Q

Vertical parabola directrix

A

y= k-p

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6
Q

Horizontal parabola Directrix

A

x=h-p

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7
Q

Latus rectum of a parabola

A

4p

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8
Q

Vertical parabola axis

A

x=h

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9
Q

Horizontal parabola axis

A

y=k

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10
Q

Horizontal ellipse equation

A

((x-h)^2/a^2) + ((y-k)^2/b^2) = 1

a >b
c^2 = a^2 - b^2

E= c/a

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11
Q

Vertical ellipse equation

A

((x-h)^2/b^2) + ((y-k)^2/a^2) = 1

a >b

c^2 = a^2 - b^2

E= c/b

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12
Q

Center of an ellipse

A

(h, k)

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13
Q

Horizontal ellipse foci

A

(h+-c, k)

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14
Q

Vertical ellipse foci

A

(h, k+-c)

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15
Q

Horizontal ellipse vertices

A

(h+-a, k)

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16
Q

Vertical ellipse vertices

A

(h, k+-a)

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17
Q

Horizontal ellipse covertices

A

(h, k+-b)

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18
Q

Vertical ellipse covertices

A

(h+-b, k)

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19
Q

Horizontal ellipse major axis

A

2a

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20
Q

Horizontal ellipse minor axis

A

2b

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21
Q

Vertical ellipse major axis

A

2b

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22
Q

Vertical ellipse minor axis

A

2a

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23
Q

Horizontal hyperbola equation

A

((x-h)^2/a^2) - ((y-k)^2/b^2) = 1

c^2 = a^2 + b^2

E = c/a

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24
Q

Vertical hyperbola equation

A

((y-k)^2/a^2) - ((x-h)^2/b^2) = 1

c^2 = a^2 + b^2

E = c/a

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25
Q

Hyperbola center

A

(h, k)

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26
Q

Horizontal hyperbola Vertices

A

(h+-a, k)

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27
Q

Vertical hyperbola vertices

A

(h, k+-a)

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28
Q

Horizontal hyperbola foci

A

(h+-c, k)

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29
Q

Vertical hyperbola foci

A

(h, k+-c)

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30
Q

Horizontal hyperbola slope

A

+- b/a

31
Q

Vertical hyperbola slopes

A

+- a/b

32
Q

A function is even if…

A

The ends face the same way

Regardless of the degree or number of zeros

33
Q

A function is odd if…

A

It’s ends face the opposite way

Regardless of the degree or number of zeros

34
Q

Decartes rule of signs

A

If a+bi is a zero of the function, then a-bi is also a zero

35
Q

Rational zero theorem

A

p/q = factors of constant/ factors of leading coefficient

p/q are possible zeros

36
Q

Vertical asymptotes

A

What makes the denominator of a function zero, and does not have removable discontinuity (hole)

37
Q

Horizontal asymptotes

A

Ax^n / Bx^m
n < m : x-axis is asymptote
n = m : fraction of leading coefficients is asymptote
n > m : no asymptote

38
Q

Direct variation

A

Where k= y/x

x1/y1 = x1/y1

39
Q

Inverse variation

A

where k= xy

x1/y2 = x2/y1

40
Q

Joint variation

A

Where y/xz = k

y1/y2 = x1z1/x2z2

41
Q

When solving rational functions and absolute value functions…

A

Always check your answer because it may not work out when you plug it back in

42
Q

Exponential functions

A 
Y= a(1+r)^t
a= initial amount
r= percent increase (expressed as a decimal)
t= time
43
Q

Logarithmic function

A

Log(b) y=x

b^x = y

44
Q

Product of powers property

A

a^m x a^n = a^(m+n)

45
Q

Power of a power property

A

(a^m)^n = a^mn

46
Q

Product of logarithms property

A

Log(b) uv = log(b) u + log(b) v

47
Q

Power of logarithms property

A

Log(b) u^v = vlog(b) u

48
Q

Quotient of powers property

A

a^m/ a^n = a^(m-n)

49
Q

Quotients of logarithms property

A

Log(b) u/v = log(b) u - log(b) v

50
Q

Characteristics

A

Numbers in front of the decimal

51
Q

Mantissa

A

Numbers behind the decimal

If it is negative add ten then subtract ten

52
Q

Antilog

A

10^x

53
Q

Interest formula

A 
A = Pe^rt
A: total amount
P: principal
r: interest rate
t: time in years
e: natural base
54
Q

Antilogrithms

A

e^b = ? Or ln? = b

55
Q

Logarithms

A

Ln (n) = ? or e^? = n

56
Q

Compounded interest formula

A 
A = P(1 + r/n)^nt
A: total amount
P: principal amount
r: interest rate ( in decimal form)
t: time in years 
n: number of times per year the interest is   compounded
57
Q

Arithmetic sequence (adding or subtracting)

A

a(n) = a1 + (n-1)d

a1: the first term
d: common difference

58
Q

Arithmetic series (sum of arithmetic sequence)

A 
S(n) = n(a1 + a(n))/ 2    or
S(n) = n[2a1 +(n-1)d]/ 2
a1: the first term
a(n): nth term 
d: common difference
S(n): the sum of the first n terms
59
Q

Geometric sequence

A

A(n) = a1 x r^(n-1)
r: common ratio; multiplier
A(n): the nth term

60
Q

Geometric series (sum of geometric sequence)

A 
S(n) = (a1-a1r^n)/ (1-r)        or
S(n) = (a1-a(n)r)/ (1-r)
a1: first term
a(n): last term in the series
r: common ratio (r doesn't equal zero)
S(n): sum of the first n terms
61
Q

Infinite geometric series

A

S = a1/ (1-r)

a1: the first term
r: common ratio. -1< r<1

62
Q

Pascal’s triangle

A 
1
1     1
1      2     1
1     3.      3.      1
1.    4.       6.      4.      1
1.    5.       10.      10.     5.     1
1.    6.        15.      20.     15.    6.      1
1.     7.        21.     35.      35.   21.     7.    1
63
Q

Permutations

A

nPr = n!/ (n-r)!

Order matters

64
Q

Combinations

A

nCr = n!/ r!(n-r)!

65
Q

Probability of inclusive events

A

P(A or B) = P(A) +P(B) - P(A and B)

66
Q

Probability of mutually exclusive events

A

P(A and B) = P(A) + P(B)

67
Q

Quartiles

A

Numbers that separate the values into four equal parts

68
Q

Outliers

A

Upper quartile + 1.5(interquartile range)
or
Lower quartile - 1.5(interquartile range)

69
Q

Probability of dependent events

A

P(A and B) = P(A) x P(B following A)

70
Q

Probability of independent events

A

P(A and B) = P(A) x P(B)

71
Q

Odds in favor of an event

A

Number of favorable outcomes/

Number of unfavorable outcomes

72
Q

Odds against an event

A

Number of unfavorable outcomes/ number of favorable outcomes

73
Q

Area of a triangle

A

A = 1/2 a x b x sinC

74
Q

Law of sines

A

SinA/ a = sinB/ b

75
Q

Law of cosines

A

a^2 = b^2 + c^2 - 2bc cosA

algebra 2 (1 decks)

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