Mathematics 10 Reviewer: Transformations and Inequalities

A comprehensive vocabulary set covering transformations on the Cartesian plane, linear inequalities, interval notation, and quadratic functions/inequalities based on the Mathematics 10 review material.

Transformation

A change in the position, size, or orientation of a figure on the coordinate plane.

Translation

A transformation that moves a point or figure without changing its size or shape.

Rule for Translation Right $h$ units

$$(x, y) \rightarrow (x + h, y)$$

Rule for Translation Left $h$ units

$$(x, y) \rightarrow (x - h, y)$$

Rule for Translation Up $k$ units

$$(x, y) \rightarrow (x, y + k)$$

Rule for Translation Down $k$ units

$$(x, y) \rightarrow (x, y - k)$$

Reflection

A transformation that flips a figure over a line called the line of reflection.

Rule for Reflection Across the x-axis

$$(x, y) \rightarrow (x, -y)$$

Rule for Reflection Across the y-axis

$$(x, y) \rightarrow (-x, y)$$

Rule for Reflection Across the origin

$$(x, y) \rightarrow (-x, -y)$$

Rotation

A transformation that turns a point or figure around a fixed point, usually the origin.

Rule for 90° Counterclockwise Rotation

$$(x, y) \rightarrow (-y, x)$$

Rule for 90° Clockwise Rotation

$$(x, y) \rightarrow (y, -x)$$

Rule for 180° Rotation

$$(x, y) \rightarrow (-x, -y)$$

Inequality

A mathematical statement that compares two quantities using $<$, $>$, $\leq$, or $\geq$.

At least

A phrase represented by the symbol $\geq$.

At most

A phrase represented by the symbol $\leq$.

Multiplication or Division by a Negative Number Property

A property of inequalities stating that the inequality sign reverses (flips) when performing these operations.

Open Circle ($\circ$)

A graphical endpoint used on a number line for inequalities with symbols $<$ or $>$, indicating the point is not included.

Closed Circle ($\bullet$)

A graphical endpoint used on a number line for inequalities with symbols $\leq$ or $\geq$, indicating the point is included.

Interval Notation Parentheses $()$

Symbols indicating that the endpoints are not included in the interval; always used for $\infty$ and $-\infty$.

Interval Notation Brackets $[]$

Symbols indicating that the endpoints are included in the interval.

Linear Inequality in Two Variables

An inequality that can have a form such as $ax + by > c$.

Dashed Boundary Line

The type of line used when graphing an inequality with $<$ or $>$ symbols.

Solid Boundary Line

The type of line used when graphing an inequality with $\leq$ or $\geq$ symbols.

Quadratic Expression

An expression with the form $ax^2 + bx + c$, where $a \neq 0$.

Parabola

The graph of a quadratic function; it opens upward if $a > 0$ and downward if $a < 0$.

Vertex

The turning point of a parabola, denoted as $(h, k)$.

Axis of Symmetry

The vertical line that divides a parabola into two mirror-image halves, given by the equation $x = h$.

Vertex x-coordinate Formula

For the standard form $y = ax^2 + bx + c$, it is calculated as $x = \frac{-b}{2a}$.

x-intercepts (Roots/Zeros)

The points where the graph crosses or touches the x-axis, found by setting $y = 0$.

Critical Numbers

The zeros of a quadratic inequality used to divide a number line into intervals for testing signs.

Vertex Form

The form of a quadratic function given by $y = a(x - h)^2 + k$.

Test Point

A coordinate, such as $(0, 0)$, substituted into an inequality to determine which region of a graph should be shaded.

System of Linear Inequalities

A set containing two or more inequalities that must be satisfied at the same time.