Exam prep Flashcards
A relation is a function if:
It pass the two test:
VLT or for every x- coordinate their is only one y-coordinate
What is domain?
Values of all the x- coordinate
What is range?
Values of all the y- coordinate
How can you tell apart a linear, quadratic, and exponential?
linear: first difference are the same
quadratic: second difference are the same
exponential: difference aren’t the same ex. 2 with a little x.
What is function notation?
It’s substituting f of x, and then solving
In y = a ( x-h)2 +k
what is “a”
If a is positive: open up
if a is negative it open down, and reflects into the x- axis
if a is a whole number it has a vertical stretch (narrower)
if it a faction or decimal it a compression ( wider)
In y= a (x-h)2 + k
what is h
if h is positive: shifts right
if h is negative: shifts left
In y= a (x-h)2 + k
what is k
if k is positive it shifts up
if k is negative it shifts down
what is the mother of all parabolas?
y=x2
How do you foil?
first, outside, inside, last
( x + 4) (2x-9)
how do you common factor?
Find the GCF
dived all number by
the GCF goes outside the bracket, and the dived number go inside.
how do you do simple trinomials
find the GCF
then do the chart method find the two numbers that multiply by a and c, but add to b
then put those number in the bracket
How do you know if it’s simple or complex trinomials?
simple their GCF is the first number “a”
complex find another GCF or do the chart method
in y= a (x-r) (x-s)
what is a
if a is positive the graph open up if it’s negative it open down
if a is > 1 it stretches’
if 0< a> a it compressed
in y= a( x-r) (x-s)
what is r and s?
r and s are the zeros
how do you find the zeros in an equation from standard from?
fully factor
then replace y for 0
and you switch the sign of the number
how do you find the difference of the square?
common factor if need be
you square root each factor
then plug it in
(x-6) (x+6)
how do you find the perfect square?
keep the sign
square root the a and c term
and plug it in with a exponent
(x-4)2 check it by multiply 2(4) (x) = the b term
what is the optimal value
is the value of the y- co-ordinate of the vertex
what is the axis of symmetry
divides the the parabola into two equal halfs
what the discriminant
b2 - 4 a c
how many roots are their if the discriminant is positive, negative or equal
positive= 2
negative= 0
equal= 1
how do you use the discriminant to find the roots?
plug into your equation
when do you use the whole discriminant formula?
when your looking for zeros, and the number are tricky like decimal
In application of quadratics how do you find the height?
you plug in 0 as you x in your equation
and then you solve
In application of quadratics how do you find when something is going to hit the ground?
your looking for the zeros
so factor if needed then plug in zeros and change the signs.
In application of quadratics how do you find the max/ min height?
add your zeros and dived by 2
this get you your x value
the plug that number into your equation
how do you solve by graphing?
this is used for standard form
Use the formula x= -b/ 2(a)
this find you the x of your vertex
then plug that x into your equation to get y of your vertex
then make a t chart, and plug in the x to find your y
graph
find your solution
when creating an equation from graphs
for factor form what do you need?
y= a (x-s) (x-r)
x= inter
y= inter
plug in to solve for “a”
when creating an equation from graphs for vertex form what do you need?
y= a (x-h) 2 +k
vertex
y= inter
plug in to solve for “a”
how do you complete the square?
stander to vertex
remove a from the first two terms
then find b/2 exponent 2
plug in that number as positive and negative
find the square root of a and the positive
now plug those number (x+3) 2 -9
multiply the negative by the outside number
then add by the out out side number to
get you equation.
what can you find with Vertex form?
y= a ( x-h) 2 +k
Vertex: can be found (h,k)
y= inter: plug in 0 to solve
axis: is h
optimal value: k
x- inter: hard to find you have to factor first
what can you find with factored form?
a(x-s) (x-r)
x- inter: switch the sign of s and r
vertex: add the x’s and then dived by 2: (x,?)
then sub to solve for for y of the vertex
y= inter: plug in 0 to slove
axis: x
optimal: y
what can you find with standard form?
ax2 + bx+ c
y= inter: plug in 0 to solve
vertex: must compete the square
x- inter: factor first
axis symmetry/ optimal value: factoring, x= -b/ 2(a)
or complete the square
how do you get from standard to vertex, and the opposite?
standard to vertex: factoring
vertex to standard: foil
how do you get from standard to factoring, and the opposite?
standard to factoring: completing the square
factoring to standard: foil
how do you get from factoring to vertex, and the opposite?
factoring to vertex: graphing
vertex to factoring: solve for “a”
where does the hyp, opp, and adj go on right triangle?
hyp: is the longest side
adj: has the right angle, and the angle
opp: is opposite from the angle
when solving for the unknowns
tan 30= X/ 10 what do you do?
you add 10 to both sides
then solve 10 tan 30
when solving for the unknowns
cos 52= 20/ x what do you do?
add y to both side
y cos 52= 30
dived the one side by the cos 52
y= 30/ cos 52
dived to solve
when solving for the unknowns
sin x = 5/12 what do you do?
do the sign inverse
-1 sin (5/12)
plug it in to solve
what the angle of elevation?
the angle looking up
what the angle of depression?
the angle looking down
what the one thing to remeber with the angle of depression and elevation
it makes the z pattern
in sine law how do you solve
sin 93/ x+= sin 55/ 17
you change the dominator
dived the both sides by number with x
to get x
in sine law how do you solve for an angle?
you change the dominator
dived both sides by that number
to sine inverse to get an angle
in cosine law how do you find SAS?
use the formula
cos < = c2-a2-b2/ -2 a b
Then you should get a fraction to do the invers
in cosine law how do you find the SSS?
use the formula
c2= a2+b2-2 ab cos <
solve get a positive number and the square root
what is peak?
the highest point on the graph
what is trough?
the lowest point on the graph
how do you know if it’s periodic?
there a repeating pattern
what is period?
the horizontal length of one cycle on the graph
what the amp?, and how do you find it?
half the distance between the max and min
max - min/ 2
what is period of a sine function?
period is 360
what is equation of axis and how do you find it?
half the distance horizontally
add the max and min and divide by 2
what is the sin function formula?
a sin ( x +<) + d
how do you graph
-2 sin ( x + 180 degrees) -1
- sin x
- strech by -2
so multiply each y by -2 - reflection in x-axis
- shift left by 180 degrees so move the point over left 180
- shift down by 1
what is the sin x
- 360, 0
-270, 1
-180, 0
-90, -1
0, 0
90, 1
180, 0
270, -1
360, 0
what the multiplication rule?
add the exponent if the base is the same
what the division rule?
subtract the exponent if the base is the same
what the power of power?
multiply the 2 exponent
6 3) 5 3x5+= 15
6 15
what the zero exponent rule?
a0= 1
how do you do fraction exponents?
the exponent goes on both the numerator and the dominator
how do you do the negative exponents?
if there a negative exponent you have to flip the number so it’s a positive , and then solve
how do you do the rational exponents?
if their a one as the numerator you put into the calculator as the denomator square root the number
if there a another number on top you put the bottom number and the square root to the exponent of the top number
In y= a. b x what does it mean
a= y= inter
b= ratio
what does an exponential graph have?
- they never touch the asymptote
- they have y-inter
- if the b
is greater than 1 it increasing
if between 0- 1 it’s decreasing
=1 : horizonatl line - if there a constant ratio
what happen when the b value is greater
the graphs becomes greater
what the ratio?
it the number the y are multiply by
what is the doubling time?
it’s the time it takes for a population to double in size
P= Po (2) t/d
what is the population of growth or decay?
The population for growth means it’s increasing
P= P0 ( 1+r) n
The population for decay means it’s decreasing
P= P0 ( 1-r)n
what is the half-life?
the half life is the time it takes for a quantity to decay to half it’s original amount.
What is simple interest?
I= prt
FV= p+ I
It’s simple so their no compounding periods or monthly payment
what is Fv compound interest?
Fv= p ( 1 + r) t
I= fv-p
it has compounding periods, but no monthly payments. it in the future so later
What is FV annuity?
Fv= R x (1 + i) n- 1/ i
it has compounding periods, monthly payments, and is in the future so later
what PV annuity?
PV= R x( 1-( 1+i)-n/ i
it has compounding periods, monthly payments, and is present so right now
what the annually compounding period?
1
what the semi- annually compounding period?
2
what the quarterly compounding period?
4
what the monthly compounding period?
12
what the daily compounding period?
356
what an amortization schedule?
a record of payment showing the interest paid, the principal, the current balance on a loan or investment
what the PV in compound interest?
Pv = fv/ ( 1+ r) n
it has compounding periods, but no monthly payment. it the present so right now
In y= a sin ( x- <) + d
what is a
if a is multiply by a number between 0 and 1 it compress
if it multiply by a number greater than 1 will compress
if there a negative it reflection into x- axis
In y= a sin ( x- <) + d
what is <
that the degrees
by adding it shift left
by subtracting it shift right
In y= a sin ( x- <) + d
what is d
by adding it shift up
by subtracting it shift down
