Set the two expressions for
equal to each other and solve for
to derive the equation of the parabola. We do this because the distance from
to
equals the distance from
to
We then square both sides of the equation, expand the squared terms, and simplify by combining like terms.
The equations of parabolas with vertex
are
when the
x -axis is the axis of symmetry and
when the
y -axis is the axis of symmetry. These standard forms are given below, along with their general graphs and key features.
Standard forms of parabolas with vertex (0, 0)
[link] and
[link] summarize the standard features of parabolas with a vertex at the origin.
Axis of Symmetry
Equation
Focus
Directrix
Endpoints of Latus Rectum
x -axis
y -axis
The key features of a parabola are its vertex, axis of symmetry, focus, directrix, and latus rectum. See
[link] . When given a standard equation for a parabola centered at the origin, we can easily identify the key features to graph the parabola.
A line is said to be tangent to a curve if it intersects the curve at exactly one point. If we sketch lines tangent to the parabola at the endpoints of the latus rectum, these lines intersect on the axis of symmetry, as shown in
[link] .
Given a standard form equation for a parabola centered at (0, 0), 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 axis of symmetry, focus, equation of the directrix, and endpoints of the latus rectum.
If the equation is in the form
then
the axis of symmetry is the
x -axis,
set
equal to the coefficient of
x in the given equation to solve for
If
the parabola opens right. If
the parabola opens left.
use
to find the coordinates of the focus,
use
to find the equation of the directrix,
use
to find the endpoints of the latus rectum,
Alternately, substitute
into the original equation.
If the equation is in the form
then
the axis of symmetry is the
y -axis,
set
equal to the coefficient of
y in the given equation to solve for
If
the parabola opens up. If
the parabola opens down.
use
to find the coordinates of the focus,
use
to find equation of the directrix,
use
to find the endpoints of the latus rectum,
Plot the focus, directrix, and latus rectum, and draw a smooth curve to form the parabola.
Graphing a parabola with vertex (0, 0) and the
x -axis as the axis of symmetry
Graph
Identify and label the
focus ,
directrix , and endpoints of the
latus rectum .
The standard form that applies to the given equation is
Thus, the axis of symmetry is the
x -axis. It follows that:
so
Since
the parabola opens right
the coordinates of the focus are
the equation of the directrix is
the endpoints of the latus rectum have the same
x -coordinate at the focus. To find the endpoints, substitute
into the original equation:
Next we plot the focus, directrix, and latus rectum, and draw a smooth curve to form the
parabola .
[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
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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