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Objectives: 1.To find the intercepts of a graph 2.To use symmetry as an aid to graphing 3.To write the equation of a circle and graph it 4.To write equations of parallel and perpendicular lines

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As a class, use your vast mathematical knowledge to define each of these words without the aid of your textbook. Graph of an Equation Solution Point InterceptsSymmetry CircleParallel Perpendicular

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graph solution points The graph of an equation gives a visual representation of all solution points of the equation.

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x -intercept The x -intercept of a graph is where it intersects the x -axis. a ( a, 0) y -intercept The y -intercept of a graph is where it intersects the y -axis. b (0, b )

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How many x- and y-intercepts can the graph of an equation have? How about the graph of a function?

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Given an equation, how do you find the intercepts of its graph? To find the x -intercepts, set y = 0 and solve for x. To find the y -intercepts, set x = 0 and solve for y.

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Find the x - and y -intercepts of y = – x 2 – 5 x.

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symmetry A figure has symmetry if it can be mapped onto itself by reflection or rotation. Click me!

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How would an understanding of symmetry help you graph an equation?

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When it comes to graphs, there are three basic symmetries: x -axis symmetry 1. x -axis symmetry: If ( x, y ) is on the graph, then ( x, - y ) is also on the graph.

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When it comes to graphs, there are three basic symmetries: y -axis symmetry 2. y -axis symmetry: If ( x, y ) is on the graph, then (- x, y ) is also on the graph.

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When it comes to graphs, there are three basic symmetries: Origin symmetry 3. Origin symmetry: If ( x, y ) is on the graph, then (- x, - y ) is also on the graph. (Rotation of 180 )

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Using the partial graph pictured, complete the graph so that it has the following symmetries: 1. x -axis symmetry 2. y -axis symmetry 3. origin symmetry

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circle The set of all coplanar points is a circle if and only if they are equidistant from a given point in the plane.

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Find the equation of points ( x, y ) that are r units from ( h, k ).

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Standard form of the equation of a circle: ( h, k ) = center point r = radius

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The point (1, -2) lies on the circle whose center is at (-3, -5). Write the standard form of the equation of the circle.

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Find the center and radius of the circle, and then sketch the graph.

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Convert the given equation to the following forms: 1.Slope-intercept form 2.Standard form

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Convert the given equation to the following forms: 1.Slope-intercept form 2.Point-slope form

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parallel lines Two lines are parallel lines iff they are coplanar and never intersect. perpendicular lines Two lines are perpendicular lines iff they intersect to form a right angle. m || n

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parallel lines Two lines are parallel lines iff they have the same slope. perpendicular lines Two lines are perpendicular lines iff their slopes are negative reciprocals.

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Write an equation of the line that passes through the point (-2, 1) and is: 1.Parallel to the line y = -3 x + 1 2.Perpendicular to the line y = -3 x + 1

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Objectives: 1.To find the intercepts of a graph 2.To use symmetry as an aid to graphing 3.To write the equation of a circle and graph it 4.To write equations of parallel and perpendicular lines

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