Section 1
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factor quadratics
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Last updated
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Date created
Mar 1, 2020
Cards (163)
Section 1
(50 cards)
factor quadratics
ax^2+bx+c b= ? + ? c= ? x ?
if you shift a line down does it change the slope
no
soh cah toa
can only be used on right triangles
word problems
define variables, choose letters that make sense, translate each phrase into math equation
when not to use calculator
-when faster to do calculation in head -requires strategic thinking not calculator
graph of quadratic with no solution
does not cross x axis -if can completely factor quadratic equation then has a solution
when squaring a number in parenthesis
can not just distribute the squared must multiply
factoring
-pull out common factors
standard form of a linear equation
Ax+By=c -can not have fractions for the coefficient -
roots
another term for a quadratic's solutions
if have 2 ratios
make both of them contain one number that is of the same value
when to use calculator
long division, extensive calculations -graph quadratics -simplify calculators and square roots
solving systems of equations elimination
p(x) - 4
the graph is shifted down 4 units -if was inside () would shift horizontally
equations where have infinite solutions
you know each side should be equal to each other so just find the factor necessary to do so
point slope form
y-y1=m(x-x1) -use if given slope and 1 point (do not need to solve for x intercept)
f(x)
means that y is a function of x, so basically as x changes y changes -fancy way of saying y
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
undefined slope
vertical line
when given a quadratic graph and need to find a point
see how far its "partner point" is away from the axis of symmetry
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
slope
difference btwn y / difference btwn x (rise over run) (up/over) -is a rate (not an average and it is not insignificant)
constant
fixed number or a variable that symbolizes a fixed number
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
completing the square
-put parenthesis around x variables -(b/2)^2 added to both sides -simplify
substitution
solve for one variable and put into second equation and solve
divided
divided, per, ratio, out
slope intercept form
y=mx+b
order of operations
pemdas
dividing fractions
-invert second number and multiply
reflecting across y axis
(-x, y)
minus
subtracted from, smaller than, less than, fewer, decreased by, difference between
addition
plus, added, sum, combined, total, increased by
greatest common factor
largest number that goes into 2+ numbers
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!
undefined
denominator must be zero
reflecting across x axis
(x, -y)
quadratic equation
(a+- b) ^2 = a^2 +- 2 ab +b^2
function notation making equation undefined
-if have lots of a series of numbers make it a variable (like x-5) -solve
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 y-intercept if you have numbers in parenthesis plus a number in the numberator
adding/subtracting fractions
-find common denominator by using common multiple -can multiply numbers
if given 1/(fraction)
it equals the reciprocal of the fraction
words meaning equal to
-was, will be, has, costs, adds up to, the same as, as much as
have a very long equation trying to isolate one variable
-look at choices, try to just eliminate options
lines that will never intersect
are parallel
multiplying fractions
-multiply straight across after simplifying fractions -simplify by putting all numbers on one line, cancelling out numbers before multiplying
when give table for g(x)
just look for where x is in table and it gives you the y value
circle equation central-radius form
(x-h)^2 + (y-k)^2=r^2 center is point (h, k)
multiplication
product of, multiplied by, twice, double, by
Section 2
(50 cards)
similarity
a shape has identical angles and proportional sides
when have circle question
draw a diagram
outlier
data point that does not follow the same overall trend as the other points
quadratic model
-u-shaped -have parabola -have vertex (min/max value) -open upward when x^2= positive, opens downward when negative coefficient
area of a circle
A=pi x r^2
g(x-1)= 3x^2+5x-7 solve
make all xs equal x + 1 and then solve
absolute value
distance a number is from 0
inequalities in 2 dimensions
-solid lines for if not < or > because line itself is included in set
1 pound equals
16 ounces
how to solve inequalities
isolate x on one side
growth and decay exponential equation
y= xo (1+r)^x r= rate of change
boundary lines
the lines on the graph of inequalities
function notation instead of f(g(x))
f circle g
axis of symmetrey
splits a shape into 2 identical parts
half planes
the shaded region on the graph
1 yard equals
3 feet
unit conversion questions
use what you learned in chemistry
polynomial factors
if divide polynomial by equation and do not get remainder then is a factor
adding inequalities
only if have the same symbol
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
polynomial functions
-function with variables raised to power higher than 1
parallel symbol
area of a triangle
A= 1/2bh
perpendicular symbol
4/5 x=
4x/5
when subtracting an expression in parentheses
distribute the negative sign to the numbers/variables in the parenthesis first
range
set of y-values on graph
commutative property
numbers can swap places and still provide the same result -addition/multiplication
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
if you want to divide an exponential equation (like from years to months) you must divide
the x, not the rate of change
"strong" relationship
good relationship but not perfect
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
growth and decay linear formula
y= kx+ xo k= rate of change
if create an equality but don't see it in the answers
you may need to just isolate one variable
associative property
different numbers groups will provide the same math result -when have multiplication/addition
can do soh cah toa
on the 90 angle
domain
the set of inputs, which corresponds to the x-values of the data points when plotted on graph
parallelograms area
A=bh
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)
infinite solutions
2+ equations have the same slope and y-intercept -if have infinite solutions the equations are dependent
key words for inequalities
-"describe all possible values of x" -"include the entire set of solutions for x" -range of values
if have a series of points
make a table
scatterplots
-make sure to only use relevant points
the coefficient should always be
the rate per unit (3 followers per post, 0.2 followers per repost)
quadrants location
left to right: 2 then 1 on top 3 then 4 on bottom
circumfrence
a circle's perimeter C=2pir
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
distance
equals rate times time
congruence
-angles, lines, and shapes can be congruent (the same) -indicated by hash marks, everything with the same number of them is congruent
regression equation
equation of the line of best fit -found in top left corner of graph
Section 3
(50 cards)
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
percent increase or decrease
amount of increase or decrease/original times 100%
f(x)=
y y intercept is f(0)
dependent equations
one equation can be manipulated algebraically to get the other one (independent equations are unable to do this)
Common Pythagorean triplets
3 4 5 and 5 12 13
45-45-90
skewed to the left
function equation
f(x)= kx+f(0) is linear g(x)=g(0)(1+r)^x
"with replacement" vs "without replacement"
-with replacement- the item chosen is returned to the original group, denominator stays the same -without replacement-the item will not be returned, number of possible outcomes will change to reflect that
measures of central tendency
mean, median, mode -can be used to represent a typical value in the data set
mean
-also called average -the sum of the values divide by the number of values
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)
probability
a fraction or decimal comparing the number of desired outcomes to the number of total possible outcomes desired outcomes/total outcomes
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
median
the value that is in the middle of the set when the values are arranged in ascending order (least to greatest)
graph of function
-if touches then parenthesis is squared, if crosses then is not
probability of a series of events
-multiply the probability of the first event by that of the second
undefined part on graph
has a circle (not filled in)
inscribed angle
An angle whose vertex is on the edge of the circle is called an inscribed angle
f(x)+a
f(x) moves up a units
x-intercept
x, 0
when looking at a graph/word problem
underline the units
if trying to find percent of majority
100- percent minority
sectors
Radii splitting a circle into pieces can also create sectors, which are parts of the circle's area.
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.
negative correlation
as 1 increases another decreases
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
30-60-90
when asked to find percent increase
you can't add/subtract percent, use the number 100
g(x-3) compared to g(x)
the graph of g(x-3) is 3 more to the right
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)
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.
f(x+a)
moves f(x) left a units
skewed to the right
equation for exponential lines
y= a (b)^x
radius
The distance from the center of a circle to its edge
y-intercept
0, y
arc
is part of a circle's circumference. Both chords and radii can cut a circle into arcs.
geometry equation
arc length/c= central angle/360= sector area/circle area
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)
chord
A line segment that connects two points on a circle
mode
the value that occurs most frequently -a set of data can have multiple modes
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.
if have a^(2/6)
simplify the fraction then convert
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
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
biweekly
divide by 26
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)
percent formula
part/whole times 100%
Section 4
(13 cards)