Test 1 Flashcards
zero factor property
factor and equal zero
root property
+-square root of other side
complete the square
- Move constant to other side
- add 1/2 b squared to both sides
- (x+1/2b)^2=constant on other side
- root property
complete the square with number in front of x^2
- Move constant
- factor out a
- complete the square
- remember to add xa to other side
- divide by a
- root property
MFCDR
quadratic formula
-b+- square root b^2-4ac / 2a
whenever you take the square root
+-
Discriminants
- number/type of solution
- found using b^2-4ac
Positive, perfect square discriminant
- 2 solutions
- rational number
positive, not perfect square discriminant
- 2 solutions
- irrational number
zero discriminant
- 1 solution
- rational number
negative discriminant
- 2 solutions
- imaginary/complex number
Distance formula
d= square root (x2-x1)^2 + (y2-y1)^2
are the points of the triangle the vertices of a right triangle?
- use distance formula
- a^2+b^2=c^2
- can also use slope- should be perpendicular (= -1)
are the points collinear?
- on the same line
- d(AB)+d(BC)=d(AC)
midpoint formula
(x1+x2/2 , y1+y2/2)
y int
x=0, solve for y
x int
y=0, solve for x
general form of the equation of a circle
ax^2+by^2+cx+dy+e=0
circle with center (h,k) and radius r has the equation
(x-h)^2 + (y-k)^2=r^2
three possibilities for the graph of a circle given the center-radius form
(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
show that (long equation) has a circle as its graph
- use complete the square to put it in center-radius form
- m greater than 0
The set of x-values are called the
domain
the set of y-values are called the
range
a relation is a
set of ordered pairs
a function is
- 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
decide whether the relation is a function
- no repeats of x
interval notation
- ( ) doesn’t include number
- [ ] includes number
interval notation of points
{ }
how to tell if a graph is a function
vertical line test
decide whether each relation defines a function
- line=yes
- parabola (x^2)=yes
- absolute value (sideways v)=no
- greater than=no
- number/x+0-#=yes- asymptotes
function notation
y=f(x)
- answer with ordered pair if possible
- make it equal to y
determine interval increasing/decreasing. Open/closed circles
- open= doesn’t include
- Closed= does include
f(x)=b
is called a constant function, and its graph is a horizontal line
- Domain is (-infinity, infinity)
- range is [y value]
vertical line
not a function but has a domain and range
standard form of a linear equation
Ax+By=C where A is positive and A, B, and C are integers with no common factor other than 1
slope formula
y2-y1 / x2-x1
different slopes
- up=positive
- down=negative
- horizontal/flat=zero (0/x)
- vertical line=undefined (x/0)
rate of change
denominator is always 1
- use slope formula and and simplify to over 1
c
cost
m
variable
x
items produced/sold
b
fixed cost
p
price
r
revenue
cost function
C(x)=mx+b
Revenue function
R(x)=px
P
profit
Profit function
R(x)-C(x)
to break even
C(x)=R(x)
point-slope form
y-y1=m(x-x1)
slope-intercept form
y=mx+b
how to make a slope-intercept equation with 2 points
- find slope
- put in point-slope form
- rearrange to slope-intercept
write the equation defining f
just an equation of a line in slope-intercept form
equation of a vertical line through the point (a,b) is
x=a
equation of a horizontal line through the point (a,b) is
y=b
two lines are parallel is they have
the same slope
two lines are perpendicular if
their slopes have a product of -1 and the slopes are negative reciprocals
find the equation in S-I form of the line that passes through a point and is parallel to this equation
- same slope
- use P-S form
- rearrange to S-I form
find the equation in S-I form of the line that passes through a point and is perpendicular to this equation
- negative reciprocal slope
- use P-S from
- rearrange to S-I form
