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