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College Algebra > Test 1 > Flashcards

Test 1 Flashcards

1
Q

zero factor property

A

factor and equal zero

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2
Q

root property

A

+-square root of other side

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3
Q

complete the square

A
  • Move constant to other side
  • add 1/2 b squared to both sides
  • (x+1/2b)^2=constant on other side
  • root property
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4
Q

complete the square with number in front of x^2

A
  • Move constant
  • factor out a
  • complete the square
  • remember to add xa to other side
  • divide by a
  • root property
    MFCDR
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5
Q

quadratic formula

A

-b+- square root b^2-4ac / 2a

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6
Q

whenever you take the square root

A

+-

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7
Q

Discriminants

A
  • number/type of solution

- found using b^2-4ac

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8
Q

Positive, perfect square discriminant

A
  • 2 solutions

- rational number

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9
Q

positive, not perfect square discriminant

A
  • 2 solutions

- irrational number

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10
Q

zero discriminant

A
  • 1 solution

- rational number

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11
Q

negative discriminant

A
  • 2 solutions

- imaginary/complex number

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12
Q

Distance formula

A

d= square root (x2-x1)^2 + (y2-y1)^2

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13
Q

are the points of the triangle the vertices of a right triangle?

A
  • use distance formula
  • a^2+b^2=c^2
  • can also use slope- should be perpendicular (= -1)
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14
Q

are the points collinear?

A
  • on the same line

- d(AB)+d(BC)=d(AC)

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15
Q

midpoint formula

A

(x1+x2/2 , y1+y2/2)

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16
Q

y int

A

x=0, solve for y

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17
Q

x int

A

y=0, solve for x

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18
Q

general form of the equation of a circle

A

ax^2+by^2+cx+dy+e=0

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19
Q

circle with center (h,k) and radius r has the equation

A

(x-h)^2 + (y-k)^2=r^2

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20
Q

three possibilities for the graph of a circle given the center-radius form

A

(x-h)^2 + (y-k)^2=m

  • if m is greater than 0, then r^2=m and the graph is a cycle with the radius square root m
  • if m=0, then the graph is a single point (h,k)
  • if m is less than 0, then no points satisfy the equation and the graph is non existent
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21
Q

show that (long equation) has a circle as its graph

A
  • use complete the square to put it in center-radius form

- m greater than 0

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22
Q

The set of x-values are called the

A

domain

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23
Q

the set of y-values are called the

A

range

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24
Q

a relation is a

A

set of ordered pairs

25
Q

a function is

A
  • a relation in which, for each distinct value of the first component of the ordered pairs, there is one and only one value of the second component
  • all x values must be different in each set of ordered pair s
26
Q

decide whether the relation is a function

A
  • no repeats of x
27
Q

interval notation

A
  • ( ) doesn’t include number

- [ ] includes number

28
Q

interval notation of points

A

{ }

29
Q

how to tell if a graph is a function

A

vertical line test

30
Q

decide whether each relation defines a function

A
  • line=yes
  • parabola (x^2)=yes
  • absolute value (sideways v)=no
  • greater than=no
  • number/x+0-#=yes- asymptotes
31
Q

function notation

A

y=f(x)

  • answer with ordered pair if possible
  • make it equal to y
32
Q

determine interval increasing/decreasing. Open/closed circles

A
  • open= doesn’t include

- Closed= does include

33
Q

f(x)=b

A

is called a constant function, and its graph is a horizontal line

  • Domain is (-infinity, infinity)
  • range is [y value]
34
Q

vertical line

A

not a function but has a domain and range

35
Q

standard form of a linear equation

A

Ax+By=C where A is positive and A, B, and C are integers with no common factor other than 1

36
Q

slope formula

A

y2-y1 / x2-x1

37
Q

different slopes

A
  • up=positive
  • down=negative
  • horizontal/flat=zero (0/x)
  • vertical line=undefined (x/0)
38
Q

rate of change

A

denominator is always 1

- use slope formula and and simplify to over 1

39
Q

c

A

cost

40
Q

m

A

variable

41
Q

x

A

items produced/sold

42
Q

b

A

fixed cost

43
Q

p

A

price

44
Q

r

A

revenue

45
Q

cost function

A

C(x)=mx+b

46
Q

Revenue function

A

R(x)=px

47
Q

P

A

profit

48
Q

Profit function

A

R(x)-C(x)

49
Q

to break even

A

C(x)=R(x)

50
Q

point-slope form

A

y-y1=m(x-x1)

51
Q

slope-intercept form

A

y=mx+b

52
Q

how to make a slope-intercept equation with 2 points

A
  • find slope
  • put in point-slope form
  • rearrange to slope-intercept
53
Q

write the equation defining f

A

just an equation of a line in slope-intercept form

54
Q

equation of a vertical line through the point (a,b) is

A

x=a

55
Q

equation of a horizontal line through the point (a,b) is

A

y=b

56
Q

two lines are parallel is they have

A

the same slope

57
Q

two lines are perpendicular if

A

their slopes have a product of -1 and the slopes are negative reciprocals

58
Q

find the equation in S-I form of the line that passes through a point and is parallel to this equation

A
  • same slope
  • use P-S form
  • rearrange to S-I form
59
Q

find the equation in S-I form of the line that passes through a point and is perpendicular to this equation

A
  • negative reciprocal slope
  • use P-S from
  • rearrange to S-I form

College Algebra (5 decks)

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