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
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits