A2T Chapter 5 Vocabulary

Rationalizing the Denominator:

The process by which a fraction is rewritten so that the denominator contains only rational numbers. A variety of techniques for rationalizing the denominator are demonstrated below. Square Roots.

Monomial:

(of an algebraic expression) consisting of one term

Trinomial:

(of an algebraic expression) consisting of three terms.

Standard Form of a Complex Number:

A complex number is any number that can be written in the standard form a + bi, where a and b are real numbers and i is the imaginary unit.

Imaginary Unit, i:

Although there are two possible square roots of any number, the square roots of a negative number cannot be distinguished until one of the two is defined as the imaginary unit, at which point and can then be distinguished.

Best-fitting Quadratic Model:

An equation that employs the variable x having the general form ax2 + bx + c = 0, where a, b, and c are constants and a does not equal zero; that is, the variable is squared but raised to no higher power.

Quadratic Formula:

The quadratic formula, is used in algebra to solve quadratic equations (polynomial equations of the second degree). The general form of a quadratic equation is , where x represents a variable, and a, b, and c are constants, with . A quadratic equation has two solutions, called roots.

Pure Imaginary Number:

a complex number of the form iy where y is a real number and i = .

Discriminant:

a function of the coefficients of a polynomial equation whose value gives information about the roots of the polynomial.

Square Root:

a number that produces a specified quantity when multiplied by itself.

Parabola:

a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.

Zero of a Function:

a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x) = 0. In other words, a "zero" of a function is an input value that produces an output of zero (0).

Binomial:

an algebraic expression of the sum or the difference of two terms.

Complex Plane:

an infinite two-dimensional space representing the set of complex numbers, especially one in which Cartesian coordinates represent the real and imaginary parts of the complex numbers.

Factoring:

another term for factorize.

Complex Conjugates:

each of two complex numbers having their real parts identical and their imaginary parts of equal magnitude but opposite sign.

Imaginary Number:

is a complex number that can be written as a real number multiplied by the imaginary unit i, [note 1] which is defined by its property i2 = −1. The square of an imaginary number bi is −b2. For example, 5i is an imaginary number, and its square is −25.

Standard Form of a Quadratic Equation/Function:

is a function that can be written in the form f(x) = ax2 + bx + c where a, b, and c are real numbers and a = 0. • Parabola: The graph of a squaring function is called a parabola.

Quadratic Inequality:

is a function whose degree is 2 and where the y is not always exactly equal to the function. These types of functions use symbols called inequality symbols that include the symbols we know as less than, greater than, less than or equal to, and greater than or equal to.

Complex Number:

is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, that satisfies the equation i2 = −1. In this expression, a is the real part and b is the imaginary part of the complex number.

Quadratic Function:

is a second-degree polynomial function of the form , where a, b, and c are real numbers and . Every quadratic function has a "u-shaped" graph called a parabola.

Completing the Square:

is a technique used to solve quadratic equations, graph quadratic functions, and evaluate integrals. This technique can be used when factoring a quadratic equation does not work or to find irrational and complex roots.

Radicand:

is the number under a radical symbol (√).

Vertex of a Parabola:

is the point where the parabola crosses its axis of symmetry. If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the "U"-shape.

Axis of Symmetry:

is the vertical line that goes through the vertex of a quadratic equation.

Radical:

of the root of a number or quantity. denoting or relating to the roots of a word.

Intercept Form of a Quadratic Function:

quadratic in intercept form just from its graph, you can use the x-intercepts and one additional point on the graph. Those three points will tell you all you need. Follow along with this tutorial to see how to use the graph of a quadratic to write its equation in intercepts form.

Zero Product Property:

simply states that if ab = 0, then either a = 0 or b = 0 (or both). A product of factors is zero if and only if one or more of the factors is zero. This is particularly useful when solving quadratic equations.

Radical Sign:

the sign √, which indicates the square root of the number following (or a higher root indicated by a preceding superscript numeral).

Vertex Form of a Quadratic Function:

to vertex form, y = a(x - h)2+ k, you use the process of completing the square. Let's see an example. Convert y = 2x2 - 4x + 5 into vertex form, and state the vertex. Equation in y = ax2 + bx + c form.

Quadratic Equation:

we define a quadratic equation as an equation of degree 2, meaning that the highest exponent of this function is 2. The standard form of a quadratic is y = ax^2 + bx + c, where a, b, and c are numbers and a cannot be 0.