Horizontal axis: The x-axis
Vertical axis: The y-axis
Origin: The point (0, 0)
Ordered pair (x, y): First number is across, second is up or down
Quadrant I: x positive, y positive (top right)
Quadrant II: x negative, y positive (top left)
Quadrant III: x negative, y negative (bottom left)
Quadrant IV: x positive, y negative (bottom right)
Where is (0, 5)?: On the y-axis, 5 units above the origin
Where is (−3, 0)?: On the x-axis, 3 units left of the origin
Which quadrant is (3, −2)?: IV
Which quadrant is (−4, −1)?: III
Which quadrant is (−2, 6)?: II
Reflect (3, 4) over the x-axis: (3, −4)
Reflect (3, 4) over the y-axis: (−3, 4)
Reflect (3, 4) through the origin: (−3, −4)
Reflect (a, b) over the line y = x: (b, a)
Translate (2, 1) by 3 right and 2 up: (5, 3)
Rotate (a, b) 90° counterclockwise about the origin: (−b, a)
Rotate (a, b) 180° about the origin: (−a, −b)
Dilate (2, 3) by scale factor 2 about the origin: (4, 6)
Distance from (0, 0) to (3, 4): 5
Distance from (1, 2) to (4, 6): 5
Midpoint of (2, 4) and (6, 8): (4, 6)
Midpoint of (−2, 3) and (4, −1): (1, 1)
Slope through (0, 0) and (2, 4): 2
Slope through (1, 5) and (3, 1): −2
Slope of y = 3x + 2: 3
Y-intercept of y = 3x + 2: 2
X-intercept of y = 2x − 6: 3
Graph of y = 5: A horizontal line
Graph of x = −2: A vertical line
Graph of y = x: A line through the origin with slope 1
Graph of y = x²: A parabola opening up with vertex at the origin
Graph of y = −x²: A parabola opening down
Graph of y = |x|: A V shape with vertex at the origin
Graph of y = 1/x: A hyperbola with branches in quadrants I and III
Graph of y = √x: Half of a sideways parabola starting at the origin
Graph of y = 2ˣ: A curve that rises quickly and passes through (0, 1)
Graph of x² + y² = 9: A circle with center (0, 0) and radius 3
Shift y = f(x) up 3: y = f(x) + 3
Shift y = f(x) right 2: y = f(x − 2)
Reflect y = f(x) over the x-axis: y = −f(x)
Reflect y = f(x) over the y-axis: y = f(−x)
Stretch y = f(x) vertically by 3: y = 3f(x)
Vertex of y = (x − 2)² + 5: (2, 5)
Axis of symmetry of y = (x − 2)² + 5: x = 2
Parallel to y = 2x + 1: Any line with slope 2
Perpendicular to y = 2x + 1: Any line with slope −1/2
Rise over run: Slope
Positive slope: The line goes up from left to right
Negative slope: The line goes down from left to right
Where lines of a system meet: The solution of the system
Line graph: Plots points joined by lines to show change over time
Scale of a graph: The value each grid mark stands for
Interval of an axis: The step between marked numbers
Latitude and longitude: A coordinate system for locations on Earth
Battleship grid: A game that uses coordinates like B7
Plotting order: Start at the origin, move across x, then up or down y
René Descartes: Introduced the Cartesian coordinate system
Polar coordinates (r, θ): Distance from the origin and angle from the positive x-axis
3D coordinates: Add a z-axis: (x, y, z)
Number of axes in a 3D grid: 3

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