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Questions and Answers
What is the characteristic shape of a quadratic graph?
What is the characteristic shape of a quadratic graph?
What is the purpose of a coordinate axis in graphing?
What is the purpose of a coordinate axis in graphing?
What is the formula to calculate the slope of a line?
What is the formula to calculate the slope of a line?
What is the equation of a line in terms of slope and intercept?
What is the equation of a line in terms of slope and intercept?
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What is the condition for two lines to be perpendicular?
What is the condition for two lines to be perpendicular?
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What is the name of the process of creating 2D shapes using a ruler and compass?
What is the name of the process of creating 2D shapes using a ruler and compass?
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What is the common property of 2D shapes?
What is the common property of 2D shapes?
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What type of graph shows exponential growth or decay?
What type of graph shows exponential growth or decay?
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Study Notes
Types of Graphs
- Linear Graphs: Straight line graphs, where the graph is a straight line.
- Quadratic Graphs: Parabolic graphs, where the graph is a U-shaped curve.
- Cubic Graphs: Graphs with a cubic equation, where the graph has a more complex shape.
- Circle Graphs: Graphs that form a circle, where every point on the graph is equidistant from a central point.
- Exponential Graphs: Graphs that show exponential growth or decay, where the graph has a rapid increase or decrease.
Drawing Graphs
- Coordinate Axes: Graphs are drawn on a pair of coordinate axes, where the x-axis is horizontal and the y-axis is vertical.
- Plotting Points: Graphs are drawn by plotting points on the coordinate axes, where each point has an x-coordinate and a y-coordinate.
- Drawing the Graph: The graph is drawn by joining the points with a line or curve, depending on the type of graph.
Geometry of Straight Lines
-
Slope: The slope of a line is a measure of how steep it is, and can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
. -
Intercept: The intercept of a line is the point where the line crosses the y-axis, and can be calculated using the formula:
y = mx + c
. -
Equation of a Line: The equation of a line can be written in the form
y = mx + c
, wherem
is the slope andc
is the intercept. - Parallel and Perpendicular Lines: Two lines are parallel if they have the same slope, and two lines are perpendicular if the product of their slopes is -1.
Geometry of 2D Shapes and Construction of Geometric Figures
- Properties of 2D Shapes: 2D shapes have properties such as number of sides, number of vertices, and internal angles.
- Construction of 2D Shapes: 2D shapes can be constructed using a ruler and compass, or using a protractor and straightedge.
- Types of 2D Shapes: Common 2D shapes include triangles, quadrilaterals, polygons, and circles.
-
Constructions: Geometric figures can be constructed using a variety of methods, including:
- Bisection: Dividing a line or angle into two equal parts.
- Perpendicular Bisector: Constructing a line perpendicular to a given line, and bisecting it.
- Angle Construction: Constructing a specific angle using a protractor and straightedge.
Types of Graphs
- Linear Graphs are straight line graphs, where the graph is a straight line, with a constant slope.
- Quadratic Graphs are parabolic graphs, where the graph is a U-shaped curve, and the graph opens upward or downward.
- Cubic Graphs are graphs with a cubic equation, where the graph has a more complex shape, and can be increasing or decreasing.
- Circle Graphs are graphs that form a circle, where every point on the graph is equidistant from a central point, called the center of the circle.
- Exponential Graphs are graphs that show exponential growth or decay, where the graph has a rapid increase or decrease, and the rate of change is proportional to the current value.
Drawing Graphs
- Coordinate Axes are a pair of lines that intersect at a right angle, where the x-axis is horizontal and the y-axis is vertical.
- Graphs are drawn by plotting points on the coordinate axes, where each point has an x-coordinate and a y-coordinate.
- The graph is drawn by joining the points with a line or curve, depending on the type of graph, and the graph can be a continuous curve or a series of discrete points.
Geometry of Straight Lines
- The slope of a line is a measure of how steep it is, and can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
, wherem
is the slope. - The intercept of a line is the point where the line crosses the y-axis, and can be calculated using the formula:
y = mx + c
, wherec
is the intercept. - The equation of a line can be written in the form
y = mx + c
, wherem
is the slope andc
is the intercept. - Two lines are parallel if they have the same slope, and two lines are perpendicular if the product of their slopes is -1.
Geometry of 2D Shapes and Construction of Geometric Figures
- 2D shapes have properties such as number of sides, number of vertices, and internal angles, which can be used to classify and describe them.
- 2D shapes can be constructed using a ruler and compass, or using a protractor and straightedge.
- Common 2D shapes include triangles, quadrilaterals, polygons, and circles, each with their own unique properties.
- Geometric figures can be constructed using a variety of methods, including:
- Bisection: Dividing a line or angle into two equal parts.
- Perpendicular Bisector: Constructing a line perpendicular to a given line, and bisecting it.
- Angle Construction: Constructing a specific angle using a protractor and straightedge.
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Description
Identify and understand different types of graphs in math, including linear, quadratic, cubic, circle, and exponential graphs. Learn to recognize their shapes and characteristics.