objectives: 1.to find the intercepts of a graph 2.to use symmetry as an aid to graphing 3.to write...
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Objectives:1. To find the intercepts of
a graph2. To use symmetry as an
aid to graphing3. To write the equation
of a circle and graph it4. 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
Intercepts Symmetry
Circle Parallel
Perpendicular
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The graphgraph of an equation gives a visual representation of all solution points solution points of the equation.
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The xx-intercept-intercept of a graph is where it intersects the x-axis.• (aa, 0)
The yy-intercept-intercept of a graph is where it intersects the y-axis.• (0, bb)
6
4
2
-2
-5 5x-intercept
y-intercept
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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 = – x2 – 5x.
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A figure has symmetrysymmetry 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:
1. xx-axis symmetry-axis symmetry: If (x, y) is on the graph, then (x, -y) is also on the graph.
, ,x y x y
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When it comes to graphs, there are three basic symmetries:
2. yy-axis symmetry-axis symmetry: If (x, y) is on the graph, then (-x, y) is also on the graph.
, ,x y x y
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When it comes to graphs, there are three basic symmetries:
3. OriginOrigin symmetry symmetry: If (x, y) is on the graph, then (-x, -y) is also on the graph.
, ,x y x y (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 symmetry2. y-axis symmetry3. origin symmetry
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The set of all coplanar points is a circlecircle 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:
2 2 2x h y k r
(h, k) = center pointr = 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.
2 22 3 25x y
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Convert the given equation to the following forms:
1.Slope-intercept form2.Standard form
36 5
4y x
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Convert the given equation to the following forms:
1.Slope-intercept form2.Point-slope form
3 7 10x y
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Two lines are parallel parallel lineslines iff they are coplanar and never intersect.
Two lines are perpendicular lines perpendicular lines iff they intersect to form a right angle.
m || n
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Two lines are parallel parallel lineslines iff they have the same slope.
Two lines are perpendicular lines 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 = -3x + 12.Perpendicular to the line y = -3x + 1
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Objectives:1. To find the intercepts of
a graph2. To use symmetry as an
aid to graphing3. To write the equation
of a circle and graph it4. To write equations of
parallel and perpendicular lines