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Give an example of a quadratic function that has zeroes at x=2 and x=4, and that takes the value 6 when x=3.

Enter your answer in the expanded form "ax^2 + bx + c", where a,b,c are replaced by appropriate numbers.

Guest Feb 13, 2018
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We can write this form, first

 

Since   x = 2  and x  = 4 are zeroes we know that it will factor as

 

y  =  a ( x - 2) (x - 4)     so.....when x  = 3  , y = 6    and we can solve for "a"

 

6 = a(3 - 2) ( 3 - 4)

 

6  = -1 a   ⇒     a = -6

 

So.....the fumction is

 

y  = -6 ( x - 2)(x - 4)

 

y  =  -6 (x^2 - 6x  + 8)

 

y = -6x^2 +36x - 48

 

 

Here's a graph to confirm this :

 

https://www.desmos.com/calculator/q6hbimtgh1

 

 

cool cool cool

CPhill  Feb 13, 2018

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