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Gravity
Terms in this set (163)
reflecting across x axis
(x, y)
reflecting across y axis
(x, y)
roots
another term for a quadratic's solutions
circle equation centralradius form
(xh)^2 + (yk)^2=r^2
center is point (h, k)
circle equation general format
ax^2+by^2+cx+dy+e=0
a and b must be the same coefficients and you must divide/factor to make them equal 1
put numbers on left side
group xs and ys together
divide left and right side by number all xs and ys share
take x term coefficient times by 1/2 square it then add to both side of equation
take y term coefficient times by 1/2 square it then add to both side of equation
find solutions then done!
when give table for g(x)
just look for where x is in table and it gives you the y value
when given a quadratic graph and need to find a point
see how far its "partner point" is away from the axis of symmetry
graph of quadratic with no solution
does not cross x axis
if can completely factor quadratic equation then has a solution
p(x)  4
the graph is shifted down 4 units
if was inside () would shift horizontally
if have 2 ratios
make both of them contain one number that is of the same value
soh cah toa
can only be used on right triangles
Math model
1) read question
2)write down info given
3)look at answers to see similarities/differences
4)should you draw a diagram
5)look for patterns
6)check that your answer answers the question asked
slope
difference btwn y / difference btwn x
(rise over run) (up/over)
is a rate (not an average and it is not insignificant)
slope intercept form
y=mx+b
point slope form
yy1=m(xx1)
use if given slope and 1 point (do not need to solve for x intercept)
lines that will never intersect
are parallel
if given 1/(fraction)
it equals the reciprocal of the fraction
if told to reflect a line on a graph
pick a point not the whole line
slope = zero
horizontal line parallel with x axis
take form y=b
standard form of a linear equation
Ax+By=c
can not have fractions for the coefficient

order of operations
pemdas
least common multiple
smallest number that is multiple of 2+ numbers
list multiples of the 2 numbers
10 10 20 30 40 50
start with number itself
greatest common factor
largest number that goes into 2+ numbers
adding/subtracting fractions
find common denominator by using common multiple
can multiply numbers
multiplying fractions
multiply straight across after simplifying fractions
simplify by putting all numbers on one line, cancelling out numbers before multiplying
dividing fractions
invert second number and multiply
factoring
pull out common factors
factor quadratics
ax^2+bx+c
b= ? + ?
c= ? x ?
solving systems of equations elimination
...
substitution
solve for one variable and put into second equation and solve
undefined slope
vertical line
f(x)
means that y is a function of x, so basically as x changes y changes
fancy way of saying y
when to use calculator
long division, extensive calculations
graph quadratics
simplify calculators and square roots
when not to use calculator
when faster to do calculation in head
requires strategic thinking not calculator
when squaring a number in parenthesis
can not just distribute the squared must multiply
words meaning equal to
was, will be, has, costs, adds up to, the same as, as much as
multiplication
product of, multiplied by, twice, double, by
divided
divided, per, ratio, out
addition
plus, added, sum, combined, total, increased by
minus
subtracted from, smaller than, less than, fewer, decreased by, difference between
word problems
define variables, choose letters that make sense, translate each phrase into math equation
equations where have infinite solutions
you know each side should be equal to each other so just find the factor necessary to do so
finding graphs with equations like
y= ay + ax + x + 1
no exponents so will be linear
put xs on one side ys on other
take out the ys/xs
divide
get answer
you know if you will make a yintercept if you have numbers in parenthesis plus a number in the numberator
if you shift a line down does it change the slope
no
have a very long equation trying to isolate one variable
look at choices, try to just eliminate options
constant
fixed number or a variable that symbolizes a fixed number
undefined
denominator must be zero
quadratic equation
(a+ b) ^2 = a^2 + 2 ab +b^2
completing the square
put parenthesis around x variables
(b/2)^2 added to both sides
simplify
function notation making equation undefined
if have lots of a series of numbers make it a variable (like x5)
solve
polynomial functions
function with variables raised to power higher than 1
polynomial factors
if divide polynomial by equation and do not get remainder then is a factor
g(x1)= 3x^2+5x7 solve
make all xs equal x + 1 and then solve
commutative property
numbers can swap places and still provide the same result
addition/multiplication
associative property
different numbers groups will provide the same math result
when have multiplication/addition
when subtracting an expression in parentheses
distribute the negative sign to the numbers/variables in the parenthesis first
absolute value
distance a number is from 0
4/5 x=
4x/5
quadrants location
left to right: 2 then 1 on top 3 then 4 on bottom
perpendicular symbol
parallel symbol
area of a triangle
A= 1/2bh
parallelograms area
A=bh
circumfrence
a circle's perimeter
C=2pir
area of a circle
A=pi x r^2
axis of symmetrey
splits a shape into 2 identical parts
congruence
angles, lines, and shapes can be congruent (the same)
indicated by hash marks, everything with the same number of them is congruent
similarity
a shape has identical angles and proportional sides
key words for inequalities
"describe all possible values of x"
"include the entire set of solutions for x"
range of values
how to solve inequalities
isolate x on one side
inequalities in graphs in one dimension
in one dimension, inequalities are graphed on a number line with a shaded region
open dot indicates that have signs < or >
if x greater than goes right, if x less than goes left
inequalities in 2 dimensions
solid lines for if not < or > because line itself is included in set
boundary lines
the lines on the graph of inequalities
half planes
the shaded region on the graph
system of inequalities
multiple equations can be combined to create a system
answer is shaded region where the shadings overlap
check shading by plugging coordinates in and seeing if they work
can do elimination or draw a graph
adding inequalities
only if have the same symbol
regression equation
equation of the line of best fit
found in top left corner of graph
line of best fit
is drawn through the data points to describe the relationship between 2 variables
have half points above and half below
gives slope (rate of change)
domain
the set of inputs, which corresponds to the xvalues of the data points when plotted on graph
range
set of yvalues on graph
outlier
data point that does not follow the same overall trend as the other points
growth and decay linear formula
y= kx+ xo
k= rate of change
growth and decay exponential equation
y= xo (1+r)^x
r= rate of change
scatterplots
make sure to only use relevant points
quadratic model
ushaped
have parabola
have vertex (min/max value)
open upward when x^2= positive, opens downward when negative coefficient
correlation coefficient
r
indicates how well a regression equation fits the data
closer r is to 1 for positive better is, closer to 1 for negative better is
distance
equals rate times time
when have circle question
draw a diagram
1 pound equals
16 ounces
1 yard equals
3 feet
"strong" relationship
good relationship but not perfect
if have a series of points
make a table
can do soh cah toa
on the 90 angle
if you want to divide an exponential equation (like from years to months) you must divide
the x, not the rate of change
g(f(2)) solve
put 2 in for f and find what x equals
put that number in for x in the g(x) equation
function notation instead of f(g(x))
f circle g
if create an equality but don't see it in the answers
you may need to just isolate one variable
the coefficient should always be
the rate per unit (3 followers per post, 0.2 followers per repost)
unit conversion questions
use what you learned in chemistry
infinite solutions
2+ equations have the same slope and yintercept
if have infinite solutions the equations are dependent
dependent equations
one equation can be manipulated algebraically to get the other one (independent equations are unable to do this)
to get rid of decimals
multiply the equation
ratio
a comparison of 1 quantity to another
you can compare a part to another part or a part to a group 1 cat : 2 dogs; 1 cat: 3 pets
if you have a:b and b:c you can get a:c
biweekly
divide by 26
Common Pythagorean triplets
3 4 5 and 5 12 13
454590
306090
radius
The distance from the center of a circle to its edge
chord
A line segment that connects two points on a circle
diameter
A chord that passes through the center of a circle. The diameter is always
the longest chord a circle can have and is twice the length of the radius.
arc
is part of a circle's circumference. Both chords and radii can cut a circle into arcs.
minor vs major arcs
If only two arcs are present, the smaller arc is called the minor arc, and the larger one is the major arc.
central angle
When radii cut a circle into multiple (but not necessarily equal) pieces, the angle at the center of
the circle contained by the radii is the central angle
sectors
Radii splitting a circle into pieces can also create sectors, which are parts of the circle's area.
geometry equation
arc length/c= central angle/360= sector area/circle area
inscribed angle
An angle whose vertex is on the edge of the circle is called an inscribed angle
tangent line
A tangent line touches a circle at exactly one point and is perpendicular to a circle's radius
at the point of contact.
percent formula
part/whole times 100%
percent increase or decrease
amount of increase or decrease/original times 100%
2 way table
table that contains data on 2 variables
can be used to make comparisons and determine whether relationships exist btwn variables (bivariate data)
if trying to find percent of majority
100 percent minority
mean
also called average
the sum of the values divide by the number of values
median
the value that is in the middle of the set when the values are arranged in ascending order (least to greatest)
mode
the value that occurs most frequently
a set of data can have multiple modes
standard deviation
a measure of how far a typical data point is from the mean
a low standard deviation means most values in the set are fairly close to the mean, a high standard deviation means there is much more spread in the data set
margin of error
a description of the max expected difference between a true value for a data pooling and a random sampling from the data pool
a lower margin of error is achieved by increasing the size of the data pool
measures of central tendency
mean, median, mode
can be used to represent a typical value in the data set
shape of data
symmetric, or skewed (asymmetric)
have a head (many data points are clustered) and a tail (where number of data points slowly decreases to zero)
skewed to the left
skewed to the right
symmetric data
if data evenly spaced, the mean and median will be the same
you can find the mean by taking the mean of the highest and lowest values ((12+2)/7)
probability
a fraction or decimal comparing the number of desired outcomes to the number of total possible outcomes
desired outcomes/total outcomes
probability of a series of events
multiply the probability of the first event by that of the second
"with replacement" vs "without replacement"
with replacement the item chosen is returned to the original group, denominator stays the same
without replacementthe item will not be returned, number of possible outcomes will change to reflect that
negative correlation
as 1 increases another decreases
if have a^(2/6)
simplify the fraction then convert
when looking at a graph/word problem
underline the units
equation for exponential lines
y= a (b)^x
xintercept
x, 0
yintercept
0, y
when asked to find percent increase
you can't add/subtract percent, use the number 100
graph of function
if touches then parenthesis is squared, if crosses then is not
g(x3) compared to g(x)
the graph of g(x3) is 3 more to the right
undefined part on graph
has a circle (not filled in)
f(x)=
y
y intercept is f(0)
function equation
f(x)= kx+f(0) is linear
g(x)=g(0)(1+r)^x
piecewise functions
a function that is defined literally by multiple pieces
open dot= not included
have different rules based on what the x value is
= means 1 point greater than or less than and equal to means closed dot, opposite means open dot
transformation
occurs when a change is made to the function's equation or graph
include translations (moving graph up/down, left/right), reflections (flips about an axis or other line), and expansions/compressions (stretching or squashing horizontally or vertically)
f(x+a)
moves f(x) left a units
f(x)+a
f(x) moves up a units
f(xa)
f(x) moves right a units
f(x)a
f(x) moves down a units
f(x)
f(x) is reflected over the x axis
f(x)
f(x) is reflected over the y axis
af(x) and a is fraction
undergoes vertical compression (fatter)
f(ax) and a is a fraction
undergoes horizontal expansion
af(x) and a is greater than 1
undergoes vertical expansion
f(ax) and a is greater than 1
undergoes horizontal compression
quadratics standard form
ax^2+bx+c
discriminant
(b^24ac)
if positive, equation has 2 distinct real solutions, if 0 then 1 real solution, if negative there are no solutions
factored form
y= a(xm)(xn)
x intercepts are m and n
vertex is halfway between m and n
vertex form
y= a(xh)^2 + k
h, k is vertex
axis of symmetry x=h
min/max is k
finding x coordinate vertex
h= b/2a
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