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Algebra Regents Review
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Gravity
Terms in this set (87)
Product
Multiply
Sum
Add
Difference
Subtract
A is subtracted from B
B - A
Linear Regression Equation
Type your data into Lists and Spreadsheets - Menu - 4: 1: 3
MOde
MOst frequent data value
Correlation Coefficient
r (what does a pirate say?)
the closer it is to 1 or -1 the closer our data is to making a straight line (Strong Correlation)
Standard deviation
Lists and Spreadsheets - Menu 4: 1: 1 Sx:= for a sample(some) or
σx:= for a population (everyone)
Multiply: (x-5)(x+5)
x²-25
Multiply: (4x-3)(4x+3)
16x²-9
Solve: (x-5)(x+3)=0
x=5, -3
Solve: (x+5)(x+3) = 0
x= -5, -3
Solve:
(2x-5)(x-1)=0
x=5/2 and 1
Solve:
(5x-2)(x-1)=0
x=2/5 and 1
What should you write when you see Round to nearest 100th
100 → . _ _
What should you write when you see Round to nearest 1000th
1000 → . _ _ _
What does f(x-h) do to f(x)
RIGHT h units
What does f(x+h) do to f(x)
LEFT h units
What does f(x)+h do to f(x)?
UP h units
What does f(x)-h do to f(x)?
DOWN h units
function
each x has exactly one y OR
each INPUT has exactly one OUTPUT
Can't have repeated x values
rational number
Any Whole number or Decimal or Fraction
can be written as a fraction of two integers (root word ratio).
NICE numbers (can be + or -)
irrational number
NOT RATIONAL (can't be written as a fraction) no repeated pattern, never ending decimal
**Usually produced when you are finding the square root of a non perfect square
roots
the same as x intercepts, zeros, solutions. set f(x)=0
domain
x values (input)
Farthest left to farthest right
range
y values (output)
Lowest low to highest high
arithmetic sequence
ADDING (or subtracting) the same value each time (linear). EQUAL DIFFERENCES
geometric sequence
Multiplying (or dividing) by the same value each time (exponential). EQUAL FACTORS
axis of symmetry
Always x = #
Runs through the vertex of a quadratic
It is DIRECTLY between the two x intercepts of a Quadratic Equation.
standard form
exponents are written in decreasing order:
Ex: 5x⁴-2x³+1
Non Ex: 5x³+10x⁵+6
leading coefficient
the NUMBER attached to the variable with the largest exponent
If you see:
"Where does f(x)=g(x)?", what should you do?
-Graph both f(x) and g(x)
-Look for where the graphs intersect. --State the x values
Perfect square trinomial
x²+6x+9 = (x+3)² or
x²+10x+25=(x+5)²
useful for complete the square!
When completing the square, what number goes in the blanks?
x²+8x+____=11+_____
16
This will make it so you can factor the left into
(x+4)²=27
You can now write the function in vertex form: f(x)=(x+4)²-27
w/ vertex at (-4,-27) or Solve by taking the square root of each side.
When completing the square, what number goes in the blank(s)?
x²+14x+____=1+_____
49
When completing the square, what number goes in the blank?
x²-20x+____=-5+_____
100
This will make it so you can rewrite as
(x-10)²=95
Factor x²+20x+100
(x+10)²
Factor x²+8x+16
(x+4)²
Factor x²-12x+36
(x-6)²
Factor: x²-2x-1
(x-1)²
Factor: x²-5x-6
(x-6)(x+1)
Factor: 4x²-81
(2x+9)(2x-9)
DIFFERENCE OF PERFECT SQUARES!! MY FAVE!
What is the next step to solve this equation:
(x-5)²=24
Square root both sides, DON'T FORGET THE PLUS OR MINUS
If you are asked to solve a quadratic, and the directions read ROUND TO THE NEAREST _____, what method should you use?
THE QUADRATIC FORMULA
Consecutive integer set up
x= first
x+1 = 2nd
x+2 = 3rd...
Consecutive EVEN or ODD integer set up
x = first
x+2 = 2nd
x+4 = 3rd...
Average rate of change
Same as SLOPE
Make a table of two points!
Change in y / change in X
Coordinates
must write an ordered pair:
( _____, _______ )
line of best fit (or Regression line)
Lists and Spreadsheets
Menu 4: 1: 3 - Linear
Menu 4: 1: A - Exponential
(same as regression)
integers
POSITIVE AND NEGATIVE whole numbers
Whole Numbers
0 + counting numbers {0,1,2,3....}
What does a Box-Plot Show us?
Min, Q1, Median, Q3, Max
Mode
MOST FREQUENT data value
Mean
"average" - not the best measure of center if you have an outlier
The calculator can compute this - Type data in lists and spreadsheets, menu 4-1-1
Median
Middle value of a data set - best measure of center if you have an outlier
RESIDUAL PLOT
if the data is a GOOD FIT the residual plot will look RANDOM (choice 2)
justify your answer
SHOW NEAT ORGANIZED MATH to support your response.
EXPLAIN
WRITE a few sentences to illustrate how you got your answer (the more clear the better)
Exponential Equation
a = start (y intercept)
b = rate of change
(if b>1 GROWTH, if 0<b<1, Decay)
don't forget to put % if needed**
If you are given a table, then look for repeated multiplication!
vertex
maximum/minimum point of a parabola
turning point
equivalent
equal to
...meaning: when graphed they will be the same.
or when a value is subbed in, they will be =
f(#)
Sub the # into "x" in the equation.
Given the quadratic y=(x-h)²+k, what is the vertex?
(h,k)
Equation
NEED AN = SIGN
Expression
no = sign necessary
Linear function
y = mx +b
*m = Slope (rate of change)
*b = starting point (y-intercept)
Repeated addition or subtraction if given a table.
solutions
Graphically: x-intercepts
Algebraically: set f(x) = 0 and solve!!!
Correlation coefficient
The "r" value from a Linear Regression. Always between -1 and 1
You can get the correlation coefficient by: Lists and Spreadsheets→Menu 4-1-3
Strong Correlation
correlation coefficient (r) is closer to -1 or 1
Weak Coorelation
correlation coefficient (r) is closer to 0
quadratic
Will look like a parabola!
Signal is: x²
Solution to a System of Equations
Intersection point.
You can solve algebraically by elimination or substitution
Infinite Solutions to a System
When the lines in a system of equations overlap!
DOTTED
When graphing y<2x+1 should you draw a solid or dotted line?
Y≥8X-7. Solid or Dotted line?
SOLID!
System of Linear Inequalities
Solution is the Overlap shaded. NOT on the dotted line.
Vertex
Turning point of a parabola!
When you take the square root...
don't forget the plus or minus!
What are the different ways you can solve a quadratic ALGEBRAICALLY.
factoring, complete the square, quadratic formula
What should you do if you graph a function on your calculator and you can't see it?
Check the table, then change the window!
when you see "CONTEXT" in a question, what should you do?
use the words from the question to include details
Talk about UNITS
What is standard deviation?
How far our data is spread apart from the Mean! The bigger the SD the more spread apart our data is
On the calculator you get it from
Menu: 4: 1:1
Sx:= (sample SD)
σx: = (population SD)
Inter Quartile Range
Q3 - Q1
When you see FACTOR COMPLETELY. What should you do?
1) LOOK FOR A GCF FIRST!
2) then factor what's left - be sure to include the GCF in your final answer!
The equation C(d)=240(1.023)^d relates the number of clovers in a field each day.
Explain what 240 and 1.023 means in context
240 - how many covers were initially in the field
1.023 -> means the number of clovers are growing by 2.3% each day (1+.023 = 1.023...)
Explain the exponential function: y=4.5(.87)^x
How do you graph a PIECEWISE FUNCTION?!
Press the Button Next to the 9 on the calculator.
Menu - View - Lined Grid.
Don't forget to OPEN circle for < or>
and CLOSED circles for ≤ or≥
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