Algebra 2 Regents Flashcards

Linear Regression

• Use the 'stat' menu to find lists and calculate linear regression.
• Ensure 'stat diagnostic' is enabled for accurate results.

Function

• A function establishes a unique relationship between each element of the domain and the range.
• Examples of non-functions include any situation where an input produces multiple outputs.

One-to-One Function

• Each range element is uniquely paired with a domain element.

Mutually Exclusive Events

• Events that cannot occur simultaneously, e.g., rolling a 2 and 6 in one die throw.

Extraneous Root

• A solution that does not satisfy the original equation or problem.

Horizontal Line Test

• A method to check if a function is one-to-one by assessing if any horizontal line intersects the graph at more than one point.

Vertical Line Test

• A graphical method to determine whether a curve represents a function.

Set Notation Example

• Represents a set with criteria, e.g., {x| x>0} defines all positive numbers.

Interval Notation

• A way to denote ranges, e.g., [ for inclusive and ( for exclusive bounds.

Completing the Square

• Use the formula (B/2)² = c for transforming quadratics into vertex form.

Axis of Symmetry Formula

• Given by -b/2a for parabolic functions.

Quadratic Formula

• Solves quadratic equations: x = (-b ± √(b² - 4ac))/2a.

Vertex Form of a Quadratic

• Written as y = a(x-h)² + k where (h, k) is the vertex.

Horizontal Shift

• Represented by the transformation f(x-h).

Vertical Shift

• Represented by the transformation f(x) + k.

Reflection Over the X-Axis

• Transformation changes (x, y) to (x, -y), negating the y-values, represented as -f(x).

Reflection Over the Y-Axis

• Transformation changes (x, y) to (-x, y), represented as f(-x).

Vertical Dilation

• Changes to a f(x), where a > 1 results in a vertical stretch.

Horizontal Dilation

• Occurs when b > 1, using the reciprocal x = (1/b)x.

Even Function

• Defined by the property f(-x) = f(x), indicating symmetry around the y-axis.

Odd Function

• Defined by the property f(-x) = -f(x), indicating symmetry around the origin.

Conjugate

• A complex number's conjugate pairs a + bi with a - bi.

Additive Inverse

• An expression of the form A + bi becomes -A - bi.

Multiplicative Inverse

• A is replaced by 1/(a + bi), ensuring the imaginary unit i isn't in the denominator.

Finding Quadratic Equation Coefficients

• Roots relate to coefficients through (R1 + R2) = -B/a and (R1 * R2) = C/a.

Vertical Asymptote

• Found where the denominator B(x) = 0.

Solving Rational Inequalities

• Steps include identifying undefined fractions, finding roots, constructing a number line, and determining satisfying values.

Horizontal Asymptote Equation

• Expressed as Y = a(x)/b(x) based on polynomial degrees.

Horizontal Asymptote Conditions

• If degree of a(x) > b(x), no asymptote exists; if <, y = 0 is the asymptote; if equal, leading coefficients yield the asymptote value.

Asymptote Transformation

• Adjusted using the formula (A/x-h) + k.

Exponential Growth Function

• Described by the formula y = a(1 + r)², where a > 0.

Exponential Decay Function

• Described by the formula y = a(1 - r)², where a > 0.

Compound Interest Formula

• A = P(1 + r/n)^(nt), with n representing the number of compounding periods per year.

Continuously Compounded Interest

• Expressed with Pe^rt, where e is Euler's number.

Logarithms

• Defined as c = a^b implies loga(c) = b.

Log Base Absence

• If no base is stated in a logarithm, the base is assumed to be 10.

Logarithmic Product Property

• logb(m) + logb(n) = logb(mn).

Logarithmic Power Property

• logb(m^n) = n logb(m).

Quotient Property

• logb(m/n) = logb(m) - logb(n).

Inverse of y = e^x

• Inverse function is y = lnx.

Alternative Exponential Growth Model

• Expressed as F(x) = ae^kt.

Alternative Exponential Decay Model

• Expressed as ae^(-kt).

Recursive Sequence

• A sequence where each term is based on the previous term(s) with a defined relationship (not fully detailed).

Test your knowledge of key concepts in Algebra 2 with these flashcards. Each card provides definitions and explanations for important terms such as linear regression and functions. Master these concepts to excel in your Algebra 2 Regents exam.