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avatar+748 

Hi my friends,

Please explain why the turning point for the following equation, is (1;5)

\(y=(2x-1)^2+5\)

 

Thank you all..

 Oct 12, 2020
 #1
avatar+27695 
+2

This is the equation of a bowl shaped  parabola with vertex   1/2  , 5     which is the turning point      ..... NOT  (1,5)

 

(2x-1)^2 + 5     can be re-written

 

4(x-1/2)^2 + 5     

 
 Oct 12, 2020
 #4
avatar+748 
0

Hi ElectricPavlov,

 

thank you for your answer, i do appreciate!!

 
juriemagic  Oct 13, 2020
 #2
avatar+111124 
+1

Hi Juriemagic,

 

\(y=(2x-1)^2+5\)

 

This is the parabola     \(y=(2x-1)^2\)      that has been lifted up 5 units.

\(y=(2x-1)^2\)    is the PARENT equation.

 

Since the PARENT equation has a double root, that means that the root is the vertex.

 

The turning point of the PARENT parabola is   

2x-1=0

2x=1

x=0.5

So the vertex of the parent equation  is  (0.5,0)

and the vertex of your equation is 5 units higher, that is   (0.5,5)

 

 

 
 Oct 12, 2020
 #3
avatar+748 
+1

oooohhhh I see,

 

gosh Melody, thank you very much for .."dismanteling" the whole thing for me...you always go the extra mile!!..I can really see your passion in helping others!!!..smiley 

 
juriemagic  Oct 13, 2020
 #5
avatar+111124 
0

Thanks Juriemagic,

 

Yes I have a passion for helping people to learn.

 

I am also grateful to you. 

You are a genuine learner, I recognize and truly appreciate that fact.

 
Melody  Oct 13, 2020

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