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II know what a discriminant is; from using it, I got -40. How will this help me determine the translation?

 Nov 18, 2019
 #1
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The discriminant  is

 

12^2  - 4 (2) (23)  =

144 - 8*23  = -40     (as you found)

 

We need the discriminant to be  =  0   for the vertex to lie on the x axis

 

Note  that   in the form   ax^2 + bx + c...  only "c"  affects the translation vertically

 

Therefore we needt to  have

 

12^2 - 4(2) c  =  0

144 - 8c  =  0

144 = 8c       divide both sides by 8

c = 18

 

So...this means that  if we translate the function down by  (23 - 18)  = 5  units....it will have its vertex on the x axis

  

See the graph  here to confirm this : https://www.desmos.com/calculator/dtqz9ykt4k

 

 

cool cool cool

 Nov 18, 2019

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