Test 1

Question 1

zero factor property

Answer 1

factor and equal zero

Question 2

root property

Answer 2

+-square root of other side

Question 3

complete the square

Answer 3

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

Question 4

complete the square with number in front of x^2

Answer 4

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

Question 5

quadratic formula

Answer 5

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

Question 6

whenever you take the square root

Answer 6

+-

Question 7

Discriminants

Answer 7

• number/type of solution

- found using b^2-4ac

Question 8

Positive, perfect square discriminant

Answer 8

• 2 solutions

- rational number

Question 9

positive, not perfect square discriminant

Answer 9

• 2 solutions

- irrational number

Question 10

zero discriminant

Answer 10

• 1 solution

- rational number

Question 11

negative discriminant

Answer 11

• 2 solutions

- imaginary/complex number

Question 12

Distance formula

Answer 12

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

Question 13

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

Answer 13

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

Question 14

are the points collinear?

Answer 14

• on the same line

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

Question 15

midpoint formula

Answer 15

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

Question 16

y int

Answer 16

x=0, solve for y

Question 17

x int

Answer 17

y=0, solve for x

Question 18

general form of the equation of a circle

Answer 18

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

Question 19

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

Answer 19

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

Question 20

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

Answer 20

(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

Question 21

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

Answer 21

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

- m greater than 0

Question 22

The set of x-values are called the

Answer 22

domain

Question 23

the set of y-values are called the

Answer 23

range

Question 24

a relation is a

Answer 24

set of ordered pairs

Question 25

a function is

Answer 25

- 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

Question 26

decide whether the relation is a function

Answer 26

- no repeats of x

Question 27

interval notation

Answer 27

- ( ) doesn't include number | - [ ] includes number

Question 28

interval notation of points

Answer 28

{ }

Question 29

how to tell if a graph is a function

Answer 29

vertical line test

Question 30

decide whether each relation defines a function

Answer 30

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

Question 31

function notation

Answer 31

y=f(x) - answer with ordered pair if possible - make it equal to y

Question 32

determine interval increasing/decreasing. Open/closed circles

Answer 32

- open= doesn't include | - Closed= does include

Question 33

f(x)=b

Answer 33

is called a constant function, and its graph is a horizontal line - Domain is (-infinity, infinity) - range is [y value]

Question 34

vertical line

Answer 34

not a function but has a domain and range

Question 35

standard form of a linear equation

Answer 35

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

Question 36

slope formula

Answer 36

y2-y1 / x2-x1

Question 37

different slopes

Answer 37

- up=positive - down=negative - horizontal/flat=zero (0/x) - vertical line=undefined (x/0)

Question 38

rate of change

Answer 38

denominator is always 1 | - use slope formula and and simplify to over 1

Question 39

c

Answer 39

cost

Question 40

m

Answer 40

variable

Question 41

x

Answer 41

items produced/sold

Question 42

b

Answer 42

fixed cost

Question 43

p

Answer 43

price

Question 44

r

Answer 44

revenue

Question 45

cost function

Answer 45

C(x)=mx+b

Question 46

Revenue function

Answer 46

R(x)=px

Question 47

P

Answer 47

profit

Question 48

Profit function

Answer 48

R(x)-C(x)

Question 49

to break even

Answer 49

C(x)=R(x)

Question 50

point-slope form

Answer 50

y-y1=m(x-x1)

Question 51

slope-intercept form

Answer 51

y=mx+b

Question 52

how to make a slope-intercept equation with 2 points

Answer 52

- find slope - put in point-slope form - rearrange to slope-intercept

Question 53

write the equation defining f

Answer 53

just an equation of a line in slope-intercept form

Question 54

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

Answer 54

x=a

Question 55

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

Answer 55

y=b

Question 56

two lines are parallel is they have

Answer 56

the same slope

Question 57

two lines are perpendicular if

Answer 57

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

Question 58

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

Answer 58

- same slope - use P-S form - rearrange to S-I form

Question 59

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

Answer 59

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