In the previous examples, we used the standard form equation of a parabola to calculate the locations of its key features. We can also use the calculations in reverse to write an equation for a parabola when given its key features.
Given its focus and directrix, write the equation for a parabola in standard form.
Determine whether the axis of symmetry is the
x - or
y -axis.
If the given coordinates of the focus have the form
then the axis of symmetry is the
x -axis. Use the standard form
If the given coordinates of the focus have the form
then the axis of symmetry is the
y -axis. Use the standard form
Multiply
Substitute the value from Step 2 into the equation determined in Step 1.
Writing the equation of a parabola in standard form given its focus and directrix
What is the equation for the
parabola with
focus
and
directrix
The focus has the form
so the equation will have the form
Graphing parabolas with vertices not at the origin
Like other graphs we’ve worked with, the graph of a parabola can be translated. If a parabola is translated
units horizontally and
units vertically, the vertex will be
This translation results in the standard form of the equation we saw previously with
replaced by
and
replaced by
To graph parabolas with a vertex
other than the origin, we use the standard form
for parabolas that have an axis of symmetry parallel to the
x -axis, and
for parabolas that have an axis of symmetry parallel to the
y -axis. These standard forms are given below, along with their general graphs and key features.
Standard forms of parabolas with vertex (
h ,
k )
[link] and
[link] summarize the standard features of parabolas with a vertex at a point
Evolution models refer to mathematical and computational representations of the processes involved in biological evolution. These models aim to simulate and understand how species change over time through mechanisms such as natural selection, genetic drift, and mutation. Evolutionary models can be u
faruk
what are the modern trends in religious behaviours
shared standards of acceptable behavior by the group or appropriate behavior in a particular institution or those behaviors that are acceptable in a society
Lucius
that is how i understood it
Lucius
examples of societal norms
Diamond
Discuss the characteristics of the research located within positivist and the interpretivist paradigm