math term 1

Law of Sines

Used to solve oblique triangles when two angles and one side are known (ASA or AAS), or two sides and a non-included angle are known (SSA). Formula: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$.

Law of Cosines

Used when two sides and the included angle are given (SAS), or all three sides are given (SSS). Formulas: $c^2 = a^2 + b^2 - 2ab \cos C$, $a^2 = b^2 + c^2 - 2bc \cos A$, $b^2 = a^2 + c^2 - 2ac \cos B$.

Bearing

Tells the direction of an object or place from a starting point, measured clockwise from North in navigation.

Cartesian Coordinate Plane

A system used to locate points precisely, consisting of two perpendicular number lines (x-axis and y-axis) intersecting at the origin $ (0,0) $.

Quadrants

Four equal regions of the Cartesian plane, divided by the x-axis and y-axis, numbered counterclockwise starting from the upper-right region: Quadrant I – $ (+,+) $; Quadrant II – $ (-,+) $; Quadrant III – $ (-,-) $; Quadrant IV – $ (+,-) $.

Transformation

The movement of a figure from one position to another on the Cartesian plane while preserving its size and shape.

Image

The new figure after a transformation, indicated by the prime symbol ($'$).

Translation

Slides a figure from one location to another without rotating or flipping it, moving every point the same distance and direction with the rule: $(x,y) \rightarrow (x+a, y+b)$.

Reflection Across the x-axis

Flips a figure over the x-axis, with the rule: $(x,y) \rightarrow (x, -y)$.

Reflection Across the y-axis

Flips a figure over the y-axis, with the rule: $(x,y) \rightarrow (-x, y)$.

Quadratic Inequality in One Variable

An inequality containing a quadratic expression with only one variable, using inequality symbols ($<, >, \le, \ge$).

Critical Points

The roots obtained from converting the quadratic inequality to an equation, dividing the number line into intervals.

Interval Notation

The notation used to express the final solution set of a quadratic inequality.

Quadratic Inequality in Two Variables

An inequality involving two variables with the highest degree of 2, comparing a quadratic expression using $<, >, \le, or \ge$.

Vertex

The turning point of the parabola $(h, k)$, representing the minimum value if $ a > 0 $ or maximum value if $ a < 0 $.

Boundary Curve

The boundary curve between the solution set and non-solutions of a quadratic inequality in two variables.

horizontal number line

called the x-axis

vertical number line

called the y-axis

origin

point where the axes intersect, (0,0)

coordinate

Used to locate points on the plane

ordered pair

pair of numbers used to represent the exact location of a point

preimage

original figure before any transformation

Parabola

A U-shaped curve that serves as the boundary on the Cartesian plane for quadratic equations and quadratic inequalities.

Opens Downward

The direction a parabola opens when the coefficient of the squared term is negative.

Opens Upward

The direction a parabola opens when the coefficient of the squared term is positive.

solid curve

A line style used for the boundary curve when an inequality includes or equal to.

broken curve

A line style used for the boundary curve when an inequality is strictly less than or greater than.

shaded region

The area on a graph that represents the complete solution set of a quadratic inequality.