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Find a polynomial function whose graph passes through ​(6,13), (9,-11), (0,5)

quilly  Mar 27, 2018
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Assuming a quadratic, we have that

y  = ax^2 + bx + c  

Since (0,5) is on the graph, c  =5

 

And we have the remaining  system

 

a(9)^2 + b(9)  + 5  =  -11

a(6)^2  + b(6) + 5  =  13     simplify

 

81a + 9b  =  -16     multiply through by  6 ⇒  486a  + 54b  =  - 96   (1)

36a + 6b   =   8      multiply through by  -9 ⇒  -324a  -54b  =  -72     (2)

 

Add (1)  and (2)

 

162a  =  -168

a  = -28/27

 

To  find b we have

36 (-28/27) + 6b  =  8   

-112/3 + 6b  = 8 

⇒  b  =  68/9

 

The function is

 

y  =  - (28/27)x^2  + (68/9)x  + 5

 

Here's a graph  with the included points  :

 

https://www.desmos.com/calculator/z4qpjyxpic

 

 

cool cool cool

CPhill  Mar 27, 2018

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