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# Turning Point

0
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5
+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
+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
+748
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Hi ElectricPavlov,

juriemagic  Oct 13, 2020
#2
+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
+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!!!..

juriemagic  Oct 13, 2020
#5
+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