Algebra 2 Terms Flashcards

Algebra 2 Terms

• Absolute Value of a Complex Number: Denoted |a+bi|, it represents the distance from the origin to the point (a,b) in the complex plane, calculated as √(a² + b²).

• Axis of Symmetry: A line that evenly divides a plane figure or a graph into two congruent, mirrored halves.

• Binomial: A type of polynomial that consists of exactly two terms.

• Completing the Square: A technique for transforming a quadratic expression into a perfect square of the form x² + bx.

• Complex Conjugate: For a complex number a+bi, its conjugate is represented as a-bi.

• Complex Number: A number that can be expressed in the form a+bi.

• Complex Plane: A coordinate system where the horizontal axis is real and the vertical axis is imaginary.

• Discriminant: In the quadratic formula, represented as b² - 4ac, it determines the nature of the roots.

• Imaginary Number: Defined as the square root of a negative number, expressed in the form bi, where b is a real number and i is the imaginary unit.

• Imaginary Part: Referring to the term b in a complex number a+bi, represented graphically on the imaginary axis.

• Imaginary Unit: Represented as i, it is used as the base in imaginary numbers.

• Maximum Value: The highest y-value point on the graph of a function.

• Minimum Value: The lowest y-value point on the graph of a function.

• Parabola: The characteristic shape of a graph representing a quadratic function.

• Quadratic Function: Expressed as ax² + bx + c, it describes a polynomial of degree 2.

• Quadratic Inequality: Inequalities that can be expressed in various forms involving a quadratic equation.

• Quadratic Model: A statistical representation using a quadratic function to fit a dataset.

• Quadratic Regression: A method used to find a quadratic model that best fits a given set of data.

• Real Part: The coefficient a in a complex number a+bi, representing the real component.

• Root of an Equation: Values of the variable that satisfy the equation, making it true.

• Standard Form: The equation format ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0.

• Trinomial: A polynomial with three distinct terms.

• Vertex Form: A way to express a quadratic function as f(x) = a(x-h)² + k, where (h,k) is the vertex.

• Vertex of the Parabola: The peak or trough point of the parabola indicating maximum or minimum values.

• Zero of a Function: Any value x such that f(x) = 0.

• Degree of a Monomial: Calculated as the sum of the exponents of the variables within the monomial.

• Degree of a Polynomial: The highest degree among the polynomial's terms.

• End Behavior: Refers to how the y-values of a function behave as the x-values approach infinity or negative infinity.

• Leading Coefficient: The coefficient of the term with the highest degree in a polynomial written in standard form.

• Local Maximum: A point where the function reaches a peak within a specified interval.

• Local Minimum: A point where the function reaches a trough within a specified interval.

• Monomial: An expression composed of a single term featuring numbers and variables raised to whole number powers.

• Polynomial: Comprises monomials combined through addition or subtraction.

• Polynomial Function: A function defined where its output follows a polynomial expression.

• Synthetic Division: A simplified method for dividing polynomials by linear binomials, only using coefficients.

• Turning Point: A point where the function changes from increasing to decreasing, or vice versa.

• Asymptote: A line that a graph approaches as the variable grows infinitely large or small.

• Common Logarithm: A logarithm with base 10.

• Exponential Decay: Described by f(x) = ab^x, where b < 1, indicating a decrease over time.

• Exponential Function: Defined as f(x) = ab^x, showcasing growth or decay based on the value of b.

• Exponential Growth: Expressed as f(x) = ab^x, where b > 1, indicating growth over time.

• Exponential Regression: A technique for fitting an exponential model to data.

• Inverse Function: A function created by swapping input and output values of a one-to-one function.

• Inverse Relation: The relation formed when pairs (x,y) are converted to (y,x), resulting in reflection across y=x.

• Logarithm: An exponent indicating how many times a base is multiplied to achieve a particular value.

• Logarithmic Equation: An equation that involves logarithms of variables.

• Natural Logarithm: A logarithm with base e, usually written as ln.

• Combined Variation: A relationship that includes both direct and inverse variation.

• Complex Fraction: Any fraction containing one or more fractions in its numerator, denominator, or both.

• Constant of Variation: The constant k in equations relating to direct, inverse, joint, or combined variation.

• Continuous Function: A function depicted by an unbroken line or curve without gaps.

• Direct Variation: A relationship between two variables, expressed as y = kx, where k is non-zero.

• Discontinuous Function: A function whose graph exhibits jumps, breaks, or holes.

• Extraneous Solution: A derived solution that does not satisfy the original equation.

• Hole in a Graph: A point that is omitted from the graph.

• Inverse Variation: Describes a relationship y = k/x, indicating an inverse connection between variables.

• Joint Variation: A relationship among three variables expressed in the form y = kxz.

• Radical Equation: An equation containing a variable within a radical expression.

• Radical Function: A function that incorporates a variable inside a radical expression.

• Radical Inequality: An inequality that features a variable within a radical.

• Rational Equation: An equation that includes one or more rational expressions.

• Rational Expression: An algebraic fraction where both the numerator and denominator are polynomials, with the denominator's degree ≤ 1.

• Rational Function: A function written as a rational expression.

• Rational Inequality: An inequality that contains one or more rational expressions.

• Square-Root Function: A function defined by a rule containing a variable under a square-root.