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] .
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?