Algebra II Midterm Review

This set of flashcards is designed to help students review key vocabulary terms and concepts from their Algebra II course as they prepare for their midterm exam.

Sequence

An ordered list of numbers following a specific pattern.

Recursive Formula

A formula that defines the terms of a sequence using previous terms.

Explicit Formula

A formula that allows finding the nth term of a sequence directly.

Function Notation

A way to denote functions using symbols like f(n) to specify the output.

Quadratic Function

A polynomial function of degree 2, typically in the form f(x) = ax² + bx + c.

Vertex

The highest or lowest point of a parabola.

Minimum Value

The smallest value of a function, occurring at the vertex of an upward-opening parabola.

Maximum Value

The largest value of a function, occurring at the vertex of a downward-opening parabola.

X-Intercept

The value of x when the function f(x) = 0.

Y-Intercept

The value of f(x) when x = 0.

Standard Form

An equation of a polynomial expressed without parentheses.

Factoring

Breaking down an expression into simpler components that, when multiplied, give the original expression.

Asymptote

A line that a graph approaches but never touches.

End Behavior

The behavior of the graph of a function as x approaches positive or negative infinity.

Leading Coefficient

The coefficient of the term with the highest degree in a polynomial.

Polynomial

A mathematical expression that consists of variables raised to whole number exponents and their coefficients.

Linear Function

A function that graphs to a straight line, usually in the form y = mx + b.

Rational Function

A function that can be expressed as the quotient of two polynomials.

Maximum Height

The highest point reached by a projectile or object thrown into the air.

Distance Formula

A formula used to determine the distance between two points in a coordinate plane.

Quadratic Formula

x = (-b ± √(b² - 4ac)) / 2a used to find the roots of quadratic equations.

Intercept Form

A way to express a linear equation where it shows the x and y intercepts.

Binomial

A polynomial with exactly two terms.

Trinomial

A polynomial with exactly three terms.

Degree of Polynomial

The highest exponent of the variable in a polynomial equation.

Constant Term

The term in a polynomial that does not contain any variables.

System of Equations

A set of two or more equations with the same variables.

Identity Function

A function that always returns the same value as its input, f(x) = x.

Absolute Value Function

A function that returns the absolute value of a number, denoted as |x|.

Transformation of Functions

Changes made to a function such as translating, reflecting, stretching, and compressing.

Horizonital Stretch

A transformation that makes a graph wider.

Vertical Compression

A transformation that reduces the height of the graph.

Reflection

Flipping a graph across a specified axis.

Function Composition

When one function is applied to the result of another function.

Domain

The set of possible input values for a function.

Range

The set of possible output values for a function.

Linear Inequality

An inequality that relates linear expressions.

Combination of Functions

The process of replacing one function in a composition with its actual output.

Piecewise Function

A function defined by different expressions based on the value of x.

Average Rate of Change

The change in the function's value divided by the change in x over an interval.

Quadratic Expression

An expression that can be written in the form ax² + bx + c.

Polynomial Long Division

Method used to divide polynomials similar to numerical long division.

Synthetic Division

A shorthand method of polynomial long division.

Leading Term

The term in a polynomial that contains the highest degree.

Vertical Shifts

Moving a graph vertically without changing its shape.

Horizontal Shifts

Moving a graph horizontally without changing its shape.

Uniform Motion

Motion with constant speed.

Rate of Change

The ratio of the change in the output of a function to the change in its input.

Graphing Calculator

A device that can plot graphs and perform calculations.

Slope-Intercept Form

A linear equation format expressed as y = mx + b.

Linear Regression

A statistical method for modeling the relationship between a dependent variable and one or more independent variables.

Fit Line

A line that best represents the data on a scatter plot.

Data Table

A method of organizing data in rows and columns.

Axis of Symmetry

A line that divides a figure into two mirror-image halves.

Inequalities

Mathematical statements used to show the relationship between expressions that are not equal.

Quartic Function

A polynomial of degree 4.

Cubic Function

A polynomial of degree 3.

Intercepts of a Graph

The points where the graph intersects the axes.

Systems of Inequalities

Sets of two or more inequalities with the same variables.

Transformation Rules

Set of guidelines that dictate how various transformations affect the graphs of functions.

Binomial Theorem

A formula for expanding a binomial raised to a power.

Numerical Coefficient

A number in front of a variable in a term.

Geometric Sequence

A sequence where each term is multiplied by a constant to obtain the next term.

Arithmetic Sequence

A sequence where each term is increased by a constant to obtain the next term.

Factorization

Expressing a polynomial as a product of its factors.

Synthetic Substitution

Using synthetic division to evaluate polynomials for given values.

Real Number Line

The line that represents all real numbers.

Transitive Property

If a = b and b = c, then a = c.

Reflection Property

The property that shows graphs can be mirrored across an axis.

Axis of Reflection

The line across which a figure is reflected.

Polynomial Inequalities

Inequalities that involve polynomial expressions.

Rational Roots Theorem

A method to find rational roots of polynomial equations.

Extreme Values

The largest and smallest values in a set or function.

Point of Inflection

A point on the curve where the curvature changes.

Complex Numbers

Numbers that have a real part and an imaginary part.

Conjugate Pair

A pair of complex numbers in the form a + bi and a - bi.

Imaginary Unit

The unit i, which satisfies the equation i² = -1.

Arithmetic Operations

The basic operations of addition, subtraction, multiplication, and division.

Graphing Approach

A method of solving equations by visualizing them on a graph.

Intersection of Functions

Points where two functions graphically meet.

Domain Restrictions

Values that are not allowed for the input of a function.

Radical Function

A function that involves roots, especially square roots.

Exponent Laws

Rules that govern the operation of exponents.

Reciprocal Function

The function that takes the reciprocal of the input.

Conic Sections

Shapes created by slicing a cone, including circles and parabolas.

Quadratic Transformation

Changes in the standard form of a quadratic to yield different graph properties.

Interval Notation

A way to describe the set of values between two endpoints.

Logarithmic Function

The inverse of an exponential function.

Statistical Measures

Values that summarize a collection of data.

Vector Representation

Using arrows to represent quantities that have both direction and magnitude.

Direct Variation

A relationship where one variable is a constant multiple of the other.

Indirect Variation

A relationship where the product of two variables is constant.

Mathematical Proof

A logical argument that verifies the truth of a mathematical statement.

Root Function

A function that involves taking roots, such as cube roots.

Binomial Distribution

A probability distribution of a binomial random variable.

Statistical Correlation

A measure of the relationship between two variables.

Probability Event

An occurrence that has a certain measure of likelihood or chance.

Adjustment to Function

Modifications made to a function to alter its output or characteristics.

Limit of a Function

The value that a function approaches as the input approaches a specific point.

Piecewise Defined Function

A function that is defined by different rules for different parts of its domain.