One report signed by two students. Both the summary sheet and work details are to be typed. Make...

Question

One report signed by two students. Both the summary sheet and work details are to be typed. Make sure you and your partner have the same problem detail. If you have two different sheets, choose either one. Attach your problem statement at the back of your solution.
All functions for this problem are quadratic.
You have two functions f(x) and g(x), f(x) passes through the points (2, 0), (0, -12), (6, 0) g(x) passes through the points (2, 1), (0, 6). (8, 1)
Find f(x), g(x) and (f g) and (-1-; (x)). State the domain of each function.
For what x's are f(x) — g(x), f(x) > g(x), and g(x) > f(x)?
Now look at the following interpretation.
If f(x) represents the average profit per 100 items sold (not including cost of quality guarantee and liability insurance per month) and g(x) represents the average cost per 100 items sold for the quality guarantee and the purchase of liability insurance, how many items (a whole number) should the store aim to sell in a single month? Why?
Note if x 2 the store is selling 200 items, it x
2.5 the store is selling 250 items
The summary contains the question (which you may reorganize and reword as long as you do not change the details) and the final solution. Additional pages contain the work.Any graphs you choose to submit vh ith the problem must be done on graph paper.
Informational note: The Domain for the application is (0, co) since .-ou cannot sell negative number of items and you would not need insurance for 0 items.
Grading: 10 points for the work (correctness. appropriateness of work, observations of connections that reduce the work needed, etc.) 5 points for presentation (typing, grammar, spelling etc.)

005_l2mfajo-vvhltefi.pdf

David · Accepted Answer

Q1.  
1st part- 
         ( )                        ( )           
Now  ( )                (   ) (     ) (   )
Hence putting (2,0) 
4a+2b+c=0 
Putting (0,-12) 
a*0+b*0+c= -12 ; 
c= -12 
Putting (6,0) 
36a+6b+c=0 
On solving for a,b,c ‘ 
a= -1, b= 8, and c= -12 
Hence  ( )            
Since f(x) is a quadratic function, hence its domain is all real numbers. 
Domain of f(x)=R 
Similarly  
         ( )                        ( )           
Now  ( )                (   ) (   ) (   )
Hence putting (2,1) 
4d+2e+f=1 
Putting (0,6) 
d*0+e*0+f= 6 ; 
f= 6
Putting (8,1) 
64d+8e+f=1 
On solving for d,e,f 
Hence   
 
  

 
     
Hence  ( )  
 
  

 
    
Since g(x) is a quadratic function, hence its domain is all real numbers. 
Domain of g(x) = R
Now(   )   ( )    ( )            (
 
  

 
   ) 
(   )   
  
  

 
     
Since (f- g)(x) is a quadratic function, hence its domain is all real numbers. 
Domain of (f- g)(x) = R 
And 
 (
 
 
 ( ))  
 ( )
 ( )
  
         
 
  

 

Since (
 
 
 ( )) is a rational quadratic function,

One report signed by two students. Both the summary sheet and work details are to be typed. Make sure you and your partner have the same problem detail. If you have two different sheets, choose either...

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