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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.

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Presentation on theme: "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."— Presentation transcript:

1 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

2 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

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

4 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 )

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

6 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.

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

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

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

10 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.

11 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.

12 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 )

13 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

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

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

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

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

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

19

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

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

22 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

23 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.

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

25 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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