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Algebra 2 Regents Preperation
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Terms in this set (54)
Finding terms in arithmetic sequence
an = a1 + (n - 1)d
Polynomial
•An algebraic expression with one or more terms
•The prefix POLY means MANY
To factor difference of perfect squares, REMEMBER:!
•The numerical coefficient has to be a perfect square
•And the exponent of each variable has to be an EVEN NUMBER.
Factoring y=ax^2+bx+c the x-box way
1)Find a*c (product of first and last term)
2)Find 2 new factors
3)Fill in the box
To factor COMPLETELY
•Check for a GCF and factor it out if possible
•Factor further if possible (different of perfect squares or a quadratic trinomial)
•Check by multiplying using the distribution property
Steps to simplify rational expressions
1)Factor what is possible in numerator & denominator
2)Reduce!
Multiplying rational expressions
1)Factor
2)Cancel all common factors in the numerator and denominator
3)Multiply straight across
Dividing rational expressions
1)Keep the first term
2)Change division to multiplication
3)Flip second term (to get reciprocal)
Standard form of quadratic function
y=ax^2+bx+c
When a>0
Opens upward :)
When a<o
Opens downwards :(
The axis of symmetry
The vertical line that cuts a function down the middle.
Finding the axis of symmetry & vertex
x=-b/2x
Quadratic equation
•ax^2+bx+c=0
•The solution(s) to this are called ROOTS or ZEROS of the function (solution are x-intercept)
To solve quadratic equation
•Rewrite equation in standard form
•Factor
•Set each factor equal to 0
•Check each solution with equation
Quadratic formula
x=-b+-√b^2-4ac/2a
To simplify radicals
•Find the largest perfect square which is a factor of the radicand
•Rewrite the square root as a product of a perfect square and another factor
•Evaluate the square root of the perfect square and write as a coefficient
•Keep the other factor as a radicand.
Ex: √50= √25 √2 => 5√2
To complete the square
1)Find one half of b-> b/2
2)Square what you got from step 1
3)Add the result to the original expression
Quadratic
Linear system is made up of a quadratic equation (palabra) and a linear equation
Cubic Functions
•Are functions with a degree of 3
•Standard form= ax^3+bx^2+cx+d (a CANNOT equal 0)
Dinding the _______ is the same as finding the ______________________
Slope, average rate of change
Natural numbers
Counting numbers greater than 0
Whole numbers
Natural numbers including 0
Integers
Positive and negative whole numbers
Rational numbers
Can be written as a fraction or a decimal which is repeating
Irrational numbers
Cannot be expressed as a fraction, they are non-repeating or non-terminating decimals.
Variable
A symbol (usually a letter) representing one or more unknown numbers
Algebraic expression
A mathematical phrase that can include numbers, variables, and operation symbols
Algebraic equation
Any sentence with an equal sign
Number sentence
A specific type of algebraic equation. It is an algebraic expression that only has numbers (NO VARIABLES)
Perimeter
2L+2W
Inequality
A mathematical statement that contains an inequality symbol
(!!! Whenever you MULTIPLY or DIVIDE an inequality by a NEGATIVE NUMBER, you MUST FLIP the inequality sign!!!)
The ___________________ depends on the ______________________
Dependent variable(output), independent variable(input)
Independent variable
X
Dependent variable
Y
Domain
All possible values of the independent variable(input)
Range
All possible values of the dependent variable(output)
Function
A relation in which each element of the domain is paired with exactly one element of range.
(If DOMAIN is chosen more than once, it is NOT A FUNCTION)
•In a function, a vertical line intersects the graph only ONCE(The vertical line test)
Function notation
y=f(x)
y=output
f=Name of function
x=input
Solid line
<= and >=
Dashed line
< and >
!Checklist for graphing a line from an equation!
•Label x and y axis
•Connect at least 2 points with a STRAIGHT EDGE
•Draw arrows at both ends of the line
•Label the line with the equation
Linear equation
An equation whose graph in a line. The points on the line are SOLUTIONS of the equation.
Special line: Vertical
If a line crosses X-AXIS we write x=?
Special line: Horizontal
If a line crosses Y_AXIS, we write y=?
Parallel line
Do NOT intersect; they have the same slope but DIFFERENT Y-INTERCEPTS.
Step function
A piece-wise function defined by CONSTANT values over its domain. The graph of a step function consists of a series of line segments.
Elimination Method
1)Line up the variables
2)Find the variable with opposite coefficient
3)Add the equations to ELIMINATE the variable
4)Solve the new equation
5)Find the other variable by substitution
6)Check!
Lines intersected
One solution, different slopes, different y-intercepts
Lines are parallel
No solution, same slopes, different y-intercepts
Lines coincide
Infinitely many solutions; same y-intercept; same slope
Substitution Method
1)Isolate a variable in at least one of the equations
2)Substitute for this variable into the other equation
3)Solve the new equation
4)Substitute the result into one of the equations to solve for the other variable
5)Check in each equation
Solution of a system of linear inequalities
Every point in the overlapping region
The negative exponent rule
1)Move the base of the negative exponent to the opposite part of the fraction
2)Change the sign from negative to positive.
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