algebra 1
vertex of a quadratic function
(-b/2a, f(-b/2a))
translation
(genetics) the process whereby genetic information coded in messenger RNA directs the formation of a specific protein at a ribosome in the cytoplasm
slope formula
(y₂- y₁) / (x₂- x₁)
multiply binomials (model)
1. Multiply the first terms. 2. Multiply the outer terms. 3. Multiply the inner terms. 4. Multiply the last terms.
graph of an inequality
A graph that shows the solution set of an inequality on a number line
vertical line
A line that goes up and down
Expression
A mathematical phrase that contains operations, numbers, and/or variables.
expressions
A mathematical phrase that contains operations, numbers, and/or variables.
inequality
A mathematical sentence that contains less than, greater than, less than or equal to, greater than or equal to, or not equal
factoring (by grouping)
A method of factoring that uses the distributive property to remove a common binomial factor of two pairs of terms.
quadratic equation (solve by factoring)
A method of solving a quadratic equation where the quadratic is set equal to zero, factored, and then solved using the zero-product property.
quadratic equation (solve by graphing)
A method of solving a quadratic equation where the quadratic is set equal to zero, graphed, and then the x-intercepts of the function are located.
Exponential form
A number is in exponential form when it is written with a base and an exponent.
Coefficient
A number multiplied by a variable in an algebraic expression.
coordinate plane
A plane that is divided into four regions by a horizontal line called the x-axis and a vertical line called the y-axis.
Add Polynomials (align like terms)
A rule that says to ADD like terms after removing all the parentheses.
subtract polynomials (align like terms)
A rule that says to SUBTRACT like terms after removing all the parentheses.
Add Polynomials (group like terms)
A rule that says you can ADD like terms in an expression.
subtract polynomials (group like terms)
A rule that says you can SUBTRACT like terms in an expression.
Multiply Binomials (squaring a binomial)
A special binomial product is the square of a binomial
function (definition)
A statement that creates a new function, specifying its name, parameters, and the statements it executes.
Variable
A symbol used to represent a quantity that can change
system of linear equations (number of solutions)
A system of linear equations usually has a single solution, but sometimes it can
domain
A taxonomic category above the kingdom level. The three domains are Archaea, Bacteria, and Eukarya.
dilation
A transformation that changes the size of an object, but not the shape.
addition/subtraction property of inequality
Adding or subtracting the same number on both sides of an inequality does not change the inequality.
functions (examples)
An example of a simple function is f(x) = x2. In this function, the function f(x) takes the value of "x" and then squares it.
dependent and independent variable (application)
An independent variable is the cause while a dependent variable is the effect in a causal research study.
quadratic equation (number of real solutions)
As we have seen, there can be 0, 1, or 2 solutions to a quadratic equation
divide polynomials (binomial divisor)
Divide the highest degree term of the polynomial by the highest degree term of the binomial
linear equation (point-slope form)
Emphasizes the slope of the line and a point on the line
transitive property for inequality
If a < b and b < c, then a < c. If a > b and b > c, then a > c.
factoring (perfect square trinomials)
If a trinomial can be written in the form a²+2ab+b² or a²-2ab+b², then it can be factored as (a+b)² or as (a-b)²
dependent and independent variable
Independent variable is on the x-axis (this is what the scientist changes) Dependent variable in on the y-axis (this is what changes in response to the independent variable
dilation (m>0)
It is a transformation that stretches or shrinks a figure from a center point, using a scale factor.
mathematical notation
Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects
linear equation (slope intercept form)
One way to write a linear equation (y = mx + b) where the product of the slope (m) and the variable (x) are added to the y-intercept (b)
transformations of parent functions
Parent functions can be transformed to create other members in a family of graphs.
translation
Process by which mRNA is decoded and a protein is produced
system of linear equations (substitution)
Step 1 : First, solve one linear equation for y in terms of x . Step 2 : Then substitute that expression for y in the other linear equation.
reflection
The bouncing back of a wave when it hits a surface through which it cannot pass.
degree of a polynomial
The degree of the term of the polynomial with the greatest degree
Absolute value
The distance a number is from zero on a number line. ALWAYS POSITIVE
system of linear equation (elimination)
The elimination method for solving systems of linear equations uses the addition property of equality
parent functions- linear,quadratic
The general form of a single-variable quadratic function is f(x) = a*x^2 + b*x + c, where a,b, and c are constants and a is non-zero.
graph of a quadratic equation
The graph of a quadratic equation is a curve (parabola) with one line of symmetry and one vertex.
quadratic function (transformational graphing)
The parent function of the quadratic family is f(x) = x2. A transformation of the graph of the parent function is represented by the function g(x) = a(x − h)2 + k, where a ≠ 0.
x-intercepts
The point(s) where a graph intersects the x-axis.
multiply binomials (sum and difference)
The product of the binomial sum and difference is equal to the square of the first term minus the square of the second term.
relations (definition and examples)
The relation defines the relation between two given sets.
Order of operations
The rules Excel follows to calculate any formula that contains two or more operators.
slopes of lines
The slope of a line is a measure of its steepness.
quotient property of radicals
The square root of a quotient equals the quotient of the square roots of the numerator and denominator
add and subtract monomial radical
There are two keys to combining radicals by addition or subtraction: look at the index, and look at the radicand.
horizontal line
This is a __________________ line. A. horizontal
Quotient of Powers Property
To divide powers with the same base, subtract their exponents
power of a power property
To find a power of a power, multiply the exponents
Power of a Product Property
To find a power of a product, find the power of each factor and multiply
Power of a Quotient Property
To find the power of a quotient, find the power of the numerator and the power of the denominator and divide
Product of Powers Property
To multiply powers with the same base, add their exponents
simplify numerical expressions
To simplify a numerical expression that has two or more operations
perpendicular lines
Two lines that intersect to form right angles
system of linear inequalities
Two or more linear inequalities using the same variables.
equivalent forms of a linear equation
Two systems of linear equations are equivalent if and only if they have the same set of solutions
linear equation (standard form)
When X and Y are variables and A,B,and C are integers
zero product property
When the product of two or more factors is zero, one of the factors must equal zero.
division property of inequality
When you divide each side of an inequality by a negative number, the inequality symbol must be reversed for the inequality to remain true.
multiplication property of inequality
When you multiply each side of an inequality by a negative number, the inequality symbol must be reversed for the inequality to remain true.
Polynomial
a mathematical expression that is the sum of a number of terms
square root
a number that when multiplied by itself equals a given number
cube root
a number that when multiplied three times equals a given number
Scientific notation
a way of writing very large or very small numbers
difference of squares (model)
a2 - b2 = (a + b)(a - b)
function notation
an equation in the form of 'f(x)=' to show the output value of a function, f, for an input value x
literal equation
an equation that contains two or more variables
Negative exponent
an exponent less than zero which causes the base and its exponent to move positions in a fraction
Zero exponent
any nonzero number raised to the zero power is 1
Multiply Binomials
apply the distributive property
Multiply Binomials (graphic organizer)
apply the distributive property
Factoring (Difference of squares)
a²-b² = (a-b) (a+b) Use Mode 5 #3 and write the opposit
divide polynomials (monomial divisor)
divide each term of the dividend by the monomial divisor
zeros
elements of a story or a picture that are not told or seen and yet offer key insights into issues that might be too sensitive to discuss or display publicly
dilation/reflection (m<0)
expanding or contracting an object without changing its shape or orientation. Reflection: flipping an object about a line without
product property of radicals
lets you take a square root of a product of numbers and break up the radical into the product of separate square roots.
parallel lines
lines in the same plane that never intersect
Multiply Polynomials
multiply each term in one polynomial by each term in the other polynomial add those answers together, and simplify if needed
containing square or cube roots
number that when multiplied by itself gives you the original number
leading coefficient
the coefficient of the first term of a polynomial in standard form
range
the difference between the highest and lowest scores in a distribution
perform first
the first time that a play or concert is performed
Factoring (Greatest Common Factor)
the greatest factor that divides two numbers
Factors of a monomial
the number(s) and/or variable(s) that are multiplied together to form a monomial
Real numbers
the set of all rational and irrational numbers
system of linear equations (graphing)
the solution is the only ordered pair that satisfies both equations (point of intersection)
slope
the steepness of a line on a graph, equal to its vertical change divided by its horizontal change
solutions or roots
the values that make an equation true
linear functions (transformational graphing)
transformed without changing the shape of the line by changing the location of the y intercept or the slope of the line.
Term
two-year period of time during which Congress meets
quadratic formula
x = -b ± √(b² - 4ac)/2a
