Algebra Final Exam Review Vocabulary

system of equations

two equations, such as y = 2x + 3 and y = -x -4

system of inequalities

two inequalities, such as y< x +3 and y >2x -1

consistent

a system where the graphs intersect or coincide

inconsistent

a system where the graph shows parallel lines

dependent

a system of equations with an infinite number of solutions

independent

a system that has exactly one solution

elimination

strategy where adding or subtracting equations will give you only one variable

substitution

strategy where one variable in an equation is solved in terms of the other variable to solve the system

monomial

a number, a variable, or a product of a number and one or more variables

binomial

the sum of two monomials

trinomial

the sum of three monomials

polynomial

a monomial or sum of monomials

degree of a monomial

the sum of the exponents of all its variables

degree of a polynomial

the greatest degree of any term in the polynomial

constant

a monomial that is a real number

FOIL method

to multiply two binomials, find the sum of the products of the first terms, the outer terms, the inner terms, and the last terms

scientific notation

a number of the form a x 10n, where 1< a < 10 and n is an integer

perfect square trinomial

a trinomial that is the square of a binomial

prime polynomial

a polynomial that can not be written as a product of two polynomials with integral coefficients

prime factorization

a whole number that is expressed as the product of factors that are all prime numbers

factoring by grouping

you can use this factoring technique if a polynomial has 4 or more terms

composite number

a whole number that has more than two factors

prime number

a whole number that has exactly two factors, 1 and itself

factoring

to express a polynomial as the product of monomials and polynomials

greatest common factor (GCF)

the greatest factor that two or more monomials have in common

axis of symmetry

the vertical line containing the vertex of a parabola

completing the square

to add a constant term to a binomial of the form x2 + bx so that the resulting trinomial is a perfect square

discriminant

in the Quadratic Formula, the expression under the radical sign, b2 - 4ac

exponential growth

an initial amount that increases by the same percent over a given period of time

exponential decay

an initial amount that decreases by the sam percent over a given period of time

exponential function

a function that can be described by the equation of the form y=ax, where a>0 and a does not equal 1

maximum

the highest point on the graph of a curve

minimum

the lowest point on the graph of a curve

parabola

the graph of a quadratic function

quadratic equation

an equation of the form ax2 + bx + c = 0, where a does not equal 0

Quadratic Formula

the solutions of a quadratic equation in the form ax2 + bx + c = 0, where a does not equal 0, are given by the formula x =[-b +(-) the square root of b2 - 4ac]/2a

quadratic function

an equation of the form y = ax2 + bx + c, where a does not equal 0

roots

the solutions of a quadratic equation

symmetry

a geometric property of figures that can be folded and each half matches the other exactly

vertex

the maximum or minimum point of a parabola

zeros

the roots, or x-intercepts, of a quadratic function

hypotenuse

the side opposite the right angle in a right triangle

radical equation

equations that contain radicals with variables in the radicand

trigonometric ratios

the ratios of the measures of two sides of a right triangle

extraneous solution

results that are not solutions to the original equation

rationalizing the denominator

a method used to eliminate radicals from the denominator of a fraction

legs

the sides of a right triangle that form the right angle

radicand

the expression that is under the radical sign

conjugate

binomials in the form of a/` + c/` and a/` -c/` (these are radical signs)

radical sign

the symbol /`, used to indicate a nonnegative square root

inverse variation

describes situations in which the values of y decrease as the values of x increase

rational expression

an algebraic fraction whose numerator and denominator are polynomials

excluded values

any value of the denominator that results in division by zero

mixed expression

an expression that is the sum of a monomial and a rational expression

complex fraction

a fraction that contains one or more fractions in the numerator or the denominator

rational equation

an equation that is made up of rational expressions