Objectives: To find the intercepts of a graph To use symmetry as an

Objectives: To find the intercepts of a graph To use symmetry as an
1.
2.
3.
4.
Objectives:
To find the intercepts
of a graph
To use symmetry as an
aid to graphing
To write the equation
of a circle and graph it
To write equations of
parallel and
perpendicular lines
Assignments:
• P. 22-23: 9-19 odd, 25,
29, 59, 62, 64, 67, 69
• P. 22: 23, 24. Ignore book
instructions.
– A) graph x-axis symmetry;
– B) graph y-axis symmetry;
– C) graph origin symmetry
• P. 35: 69, 71
• Homework Worksheet
• Read P. 40-47; A2-A3
Graph of an Equation
Solution Point
Intercepts
Symmetry
Circle
Parallel
Perpendicular
You will be able to find the intercepts of a graph
The graph of an
equation gives a
visual representation
of all solution points
of the equation.
The x-intercept of a
graph is where it
intersects the x-axis.
• (a, 0)
The y-intercept of a
graph is where it
intersects the y-axis.
• (0, b)
6
4
y-intercept
2
-5
x-intercept
5
-2
How many x- and y-intercepts can the graph of
an equation have? How about the graph of a
function?
Given an equation, how do you find the
intercepts of its graph?
To find the x-intercepts
To find the y-intercepts
Set y = 0 and
solve for x
Set x = 0 and
solve for y
Find the x- and y-intercepts of y = – x2 – 5x.
You will be able
to use
symmetry to
help you graph
an equation.
A figure has
symmetry if it can
be mapped onto
itself by reflection
or rotation.
Click me!
How would an
understanding of
symmetry help you
graph an equation?
When it comes to graphs,
there are three basic
symmetries:
1. x-axis symmetry: If
(x, y) is on the graph,
then (x, −y) is also on
the graph.
 x, y    x,  y 
When it comes to graphs,
there are three basic
symmetries:
2. y-axis symmetry: If
(x, y) is on the graph,
then (−x, y) is also on
the graph.
 x, y     x, y 
When it comes to graphs,
there are three basic
symmetries:
3. Origin symmetry: If
(x, y) is on the graph,
then (−x, −y) is also on
the graph.
 x, y     x,  y 
(Rotation of 180)
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
It’s pretty easy to tell if a graph has a particular
symmetry, but what if you only know the
equation?
Symmetry
Algebraic Test
x-axis
Plugging in –y for y gives the same equation
y-axis
Plugging in –x for x gives the same equation
origin
Plugging in –y for y and –x for x gives the same
equation
Determine which, if any, symmetry the graph of
each equation should display.
1. y = 2x2 – 3
2. y = 1/x
The set of all coplanar
points is a circle if
and only if they are
equidistant from a
given point in the
plane.
Find the equation of points (x, y) that are r units
from (h, k).
Standard form of the equation of a circle:
 x  h   y  k 
2
2
(h, k) = center point
r = radius
r
2
The point (1, −2) lies on the circle whose center
is at (−3, −5). Write the standard form of the
equation of the circle.
The previous question
asked for the equation
of a circle given the
center and a point on
the circle. What other
collection of points
could a question give
you to enable you to
write the equation of a
circle?
Find the center and radius of the circle, and then
sketch the graph.
 x  2    y  3
2
2
 25
Convert the given equation to the following
forms:
3
y  6   x  5
4
1. Slope-intercept form
2. Standard form
Convert the given equation to the following
forms:
3 x  7 y  10
1. Slope-intercept form
2. Point-slope form
Two lines are parallel
lines iff they are
coplanar and never
intersect.
m || n
Two lines are
perpendicular lines iff
they intersect to form
a right angle.
Two lines are parallel
lines iff they have the
same slope.
Two lines are
perpendicular lines iff
their slopes are
negative reciprocals.
Write an equation of the line that passes
through the point (−2, 1) and is:
1. Parallel to the line y = −3x + 1
2. Perpendicular to the line y = −3x + 1
Find the value of k: if the line through the points
(2k + 1, –4) and (5, 3 – k) is parallel to the line
through the points (–4, –9) and (2, –3).
1.
2.
3.
4.
Objectives:
To find the intercepts
of a graph
To use symmetry as an
aid to graphing
To write the equation
of a circle and graph it
To write equations of
parallel and
perpendicular lines
Assignments:
• P. 22-23: 9-19 odd, 25,
29, 59, 62, 64, 67, 69
• P. 22: 23, 24. Ignore
book instructions.
– A) graph x-axis
symmetry;
– B) graph y-axis
symmetry;
– C) graph origin
symmetry
• P. 35: 69, 71
• Homework Worksheet
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