Given a standard form equation for a parabola centered at (
h ,
k ), sketch the graph.
Determine which of the standard forms applies to the given equation:
or
Use the standard form identified in Step 1 to determine the vertex, axis of symmetry, focus, equation of the directrix, and endpoints of the latus rectum.
If the equation is in the form
then:
use the given equation to identify
and
for the vertex,
use the value of
to determine the axis of symmetry,
set
equal to the coefficient of
in the given equation to solve for
If
the parabola opens right. If
the parabola opens left.
use
and
to find the coordinates of the focus,
use
and
to find the equation of the directrix,
use
and
to find the endpoints of the latus rectum,
If the equation is in the form
then:
use the given equation to identify
and
for the vertex,
use the value of
to determine the axis of symmetry,
set
equal to the coefficient of
in the given equation to solve for
If
the parabola opens up. If
the parabola opens down.
use
and
to find the coordinates of the focus,
use
and
to find the equation of the directrix,
use
and
to find the endpoints of the latus rectum,
Plot the vertex, axis of symmetry, focus, directrix, and latus rectum, and draw a smooth curve to form the parabola.
Graphing a parabola with vertex (
h ,
k ) and axis of symmetry parallel to the
x -axis
Graph
Identify and label the
vertex ,
axis of symmetry ,
focus ,
directrix , and endpoints of the
latus rectum .
The standard form that applies to the given equation is
Thus, the axis of symmetry is parallel to the
x -axis. It follows that:
the vertex is
the axis of symmetry is
so
Since
the parabola opens left.
the coordinates of the focus are
the equation of the directrix is
the endpoints of the latus rectum are
or
and
Next we plot the vertex, axis of symmetry, focus, directrix, and latus rectum, and draw a smooth curve to form the parabola. See
[link] .
Graphing a parabola from an equation given in general form
Graph
Identify and label the vertex, axis of symmetry, focus, directrix, and endpoints of the latus rectum.
Start by writing the equation of the
parabola in standard form. The standard form that applies to the given equation is
Thus, the axis of symmetry is parallel to the
y -axis. To express the equation of the parabola in this form, we begin by isolating the terms that contain the variable
in order to complete the square.
It follows that:
the vertex is
the axis of symmetry is
since
and so the parabola opens up
the coordinates of the focus are
the equation of the directrix is
the endpoints of the latus rectum are
or
and
Next we plot the vertex, axis of symmetry, focus, directrix, and latus rectum, and draw a smooth curve to form the parabola. See
[link] .
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills