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Algebra Regents
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Gravity
Key Concepts:
Terms in this set (65)
Polynomials
An expression with more than 1 term.
Multiplying Polynomials
Double Distributive, Box Method, FOIL
Steps for Double Distributive
Rewrite the problem with one parentheses broken up, and the 2nd next to each part. Distribute.
(x+2)(x+4)
x(x+4) + 2(x+4)
Box Method
Similar to Punnett Squares. Used to multiply polynomials.
FOIL
First Outer Inner Last
(x+2)(x+4) F: xx 0: 4x I:2x L:2(4)
Only works with 2 binomials.
Adding and Subtracting Polynomials
Combine Like Terms
Like terms
Same variable and same exponent. I.e. 2x & 6x
Measures of Central Tendency
Mean, Median, Mode
Median (2nd Quartile)
Middle number when the numbers are in order from least to greatest.
Mean
Sum of data divided by the number of pieces of data. 'Traditional average'
Mode
Most frequently occurring.
Range(statistics)
Difference between the Maximum and the Minimum
Linear Regression(Use)
Gives you the equation to the line of best fit.(least squares line)
Linear Regression (steps)
Requires 2 lists. L1 x-values, and L2 y-values, Stats -> Calc -> LinReg(4)
Lower Quartile (1st Quartile)
Middle number of the data between the Min and the Median. Data needs to be ordered.
Upper Quartile (3rd Quartile)
Middle number of the data found between the Median and the Maximum. Data needs to be ordered.
1-variable-stats(calc)(use)
Requires 1 list, shows the mean, Min, Q1, Median, Q3, Max
1-variable stats(calc)(steps)
Input List, Stat -> Calc -> (1) 1-variable stats. Scroll down for some information.
Piece-wise Functions
Graphs that have at least 2 rules(equations) for different parts of the domain.
Piece-wise functions (things to be careful of)
Open and closed end points based on the inequality. <,> open dots, equal to inequalities get closed dots.
Domain
All possible inputs for a function, refer to the x-values.
Function
Is when every input has 1 and only 1 output. Passes the vertical line test.
Inequalities(Graphing)
<,> dashed line
Less than or equal to, or greater than or equal to is a solid line.
Shade one side of the line based on the inequality. Test point, if possible (0,0)
Write S where the shading crosses
Solving inequalities
When multiplying or dividing by negative numbers, flip the the inequality sign.
<
less than
>
greater than
Factoring
Undoes multiplication, creates equivalent expressions
Factoring (Methods)
P|S chart[A/M], GCF, DOTS
GCF (Steps)
Greatest Common Factor
Undoes distributive property
Creates 1 set of parenthesis
Answers look like GCF(something)
i.e
18x + 6y + 4 = 2(9x + 3y + 2)
DOTS (Steps)
Difference Of Two perfect Squares
Binomials (2 terms)
Both terms are perfect squares
Requires subtraction sign
Creates 2 sets of parenthesis
P|S chart[A/M] (steps)
product/sum chart
trinomials (3 terms) ax^2+ bx+c
product has to multiply to C
add up to B
creates two sets of ( )'s
Multiply or Divide with 2 positive numbers or 2 negative numbers the result
has to be positive.
Multiply or Divide with 1 positive and 1 negative number the result
is negative.
Distributive Property
Type of Multiplication
a(b + c) = ab + ac
2(x + 3) = 2x + 6
Quadratic Functions(Graph)
Is in the shape of parabola.
Vertex of a Parabola
Called the turning point. The Axis of Symmetry goes through the vertex.
General form of a Quadratic
Quadratic Formula
Found on the Reference Sheet
Always finds your roots.
Ways to Solve Quadratic functions
Quadratic Formula
Graphing
Factoring
Completing the Square
Solving a Quadratic with graphing
Roots are found where the parabola crosses the x-axis.
Axis of Symmetry Formula
x = -b/2a
Axis of Symmetry
A vertical line that cuts the parabola into two equal parts and goes through the vertex.
System of Equations
At least 2 equations with the same variables.
Ways to solve System of equations
Substitution, Elimination, Graphing
Algebraic ways to solve system of equations
Substitution and Elimination
System of Equations Graphing Setup
Both y = mx + b, easy to graph
System of equations elimination setup
Both equations have both variables on the same side.
i.e 2x + 4y = 30, -2x - 3y = 20
System of equations Substitution Setup
At least one equation is solved for a variable(x or y is alone)
i.e y = x + 2, 8x -4y = 50
Solving a System of Equations with graphing (steps)
1) Graph each line
2) Point of intersection is the solution to the system of equations.
Solving a System of Equations with elimination (steps)
*Multiply to create equal coefficients(not always needed)
1) Add the 2 equations together, at least 1 variable cancels out.
2) Solve the remaining equation.
3) Go back and do it again eliminating the other variable, or use substitution to find 2nd variable.
Solving a system of Equations with substitution (steps)
1) Replace(substitute) one variable for it's equivalent expression.
2) Solve the remaining equation
3) Substitute the known value, and solve for the 2nd variable.
Linear Function Graph
Is a line
Linear Function equation
y = mx + b, m is slope, b is y-intercept
Linear Function graphing (steps with calculator)
1*) Solve for y =
2) Plug into y= on calculator
3) Go to table. 2nd + graph
4) Plot the points from the table
Linear Function graphing(steps by hand)
1*) Solve for y =
2) Identify slope(m), and y-int(b)
3) Plot y-int (0,b)
4) Use slope to move and create other points
Slope Formula
m = y2-y1 /(x2-x1)
Exponential Functions
Variable is in the exponent spot. Rapid growth or shrinking.
Exponential Growth Formula
y= C(1+r)^x, C = initial amount, r = rate(as a decimal)
Exponential Decay Formula
y= C(1-r)^x, C = initial amount, r = rate(as a decimal)
Integers
Whole numbers, no fractions or decimals.
Irrational Numbers
Non-terminating and Non-repeating decimals, cannot be written as a fraction.
Rational Numbers
Numbers that can be written as a fraction.
Absolute Value(calculator)
Located in the math menu, sub menu num.
Correlation coefficient
Describes how well a line of best fit, fits the data. Values closer to 1 and -1 are stronger, correlation gets weaker as you get closer to 0.
Finding correlation coefficient (calculator)
Turn on Diagnostics, One method under the mode menu, or in the catalog(2nd 0). Run linear regression.
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