Answer: 
Step-by-step explanation:
Given: A mirror with a parabolic cross section is used to collect sunlight on a pipe located at the focus of the mirror.
The pipe is located 8 inches from the vertex of the mirror.
Assume the vertex is at the origin.
If the parabola opens upwards
then the coordinates of focus= (0,8)
We know that equation of parabola with focus (0,a) and open upards is of the form (vertex=(0,0)) is

Substitute the value of a=8 in equation, we get


Therefore, equation of the parabola that models the cross section of the mirror is 
Answer:
Step-by-step explanation:
Given

Required
Which of the above is a quadratic function
A quadratic function has the following form;

So, to get a quadratic function from the list of given options, we simply perform a comparative test of each function with the form of a quadratic function

This is not a quadratic function because it follows the form
and this is different from 
This function has an exact match with 
By comparison; 

This is not a quadratic function because it follows the form
and this is different from 

This is not a quadratic function because it follows the form 
Unlike the quadratic function where 
So, from the list of given options, only
satisfies the given condition
Question
Which expression is equivalent to
. Assuming 
Answer:

Step-by-step explanation:
Given

Required:
Simplify
To simplify this, we start by splitting each individual function

From laws of indices

SO, the above expression can also be expressed the same way



From laws of indices,

So,


Hence,
is equivalent to 