CPM Algebra 2 Chapter 2 Review

Vocabulary flashcards covering core concepts from CPM Algebra 2 Chapter 2 Review, including systems of equations, exponential models, parabola transformations, circle equations, and sequence representations.

System of Equations

A collection of two or more equations containing the same set of variables that are solved together to identify their common solution point(s).

Exponential Function

A mathematical function of the form $y = a(b)^x$, where $a$ is the initial value, $b$ is the growth or decay multiplier, and the variable $x$ appears as an exponent.

Exponential Growth

A pattern of increase modeled by the equation $y = a(1 + r)^t$, where a quantity grows at a fixed annual or periodic percentage rate $r$.

Exponential Decay

A pattern of decrease modeled by the equation $y = a(1 - r)^t$, where a quantity diminishes by a fixed percentage rate $r$ over each successive time interval.

Graphing Form of a Quadratic (Vertex Form)

A quadratic equation written in the form $y = a(x - h)^2 + k$, where $(h, k)$ represents the vertex of the parabola and $a$ determines the vertical stretch, compression, and orientation.

Standard Form of a Quadratic

A quadratic relation expressed in the form $y = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants and $a \neq 0$.

Completing the Square

An algebraic method used to convert a quadratic expression from standard form $y = ax^2 + bx + c$ into graphing form $y = a(x - h)^2 + k$.

Line of Symmetry

The vertical line defined by $x = h$ passing through the vertex of a vertical parabola that divides it into two congruent, mirror-image halves.

Standard Form of a Circle

The equation $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ designates the center coordinates and $r$ is the radius of the circle.

Locator Point

A specified reference point (such as a vertex, inflection point, or endpoint) that serves as the anchor when translating and transforming a parent graph.

Transformed Exponential Graph (Problem 16a)

The graph of the parent exponential function $y = 2^x$ shifted down $2$ units, defined by the equation $y = 2^x - 2$, with a horizontal asymptote at $y = -2$.

Transformed Hyperbola Graph (Problem 16b)

The graph of the parent rational function $y = \frac{1}{x}$ translated left $2$ units, defined by the equation $y = \frac{1}{x + 2}$, with a vertical asymptote at $x = -2$.

Transformed Parabola Graph (Problem 16c)

The graph of the parent quadratic function $y = x^2$ shifted downward $4$ units, described by the equation $y = x^2 - 4$, with vertex at $(0, -4)$.

Transformed Cubic Graph (Problem 16d)

The graph of the parent cubic function $y = x^3$ shifted right $2$ units, described by the equation $y = (x - 2)^3$, with an inflection locator point at $(2, 0)$.

Explicit Equation (Sequence)

A mathematical formula that gives the value of the $n$-th term $t(n)$ directly in terms of the position $n$, without requiring calculation of preceding terms.

Recursive Equation (Sequence)

A sequence specification that provides the starting term (such as $t(1)$) and a rule determining any succeeding term $t(n + 1)$ from the preceding term $t(n)$.