Hi my friends,

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

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

Thank you all..

juriemagic Oct 12, 2020

#1**+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

ElectricPavlov Oct 12, 2020

#2**+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)

Melody Oct 12, 2020

#3**+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