What is the vertex of #y= 2x^2 - 4x + 3#?

Given: #y=2x^2-4x+3.............................(1)#

Let the coordinates of the vertex be #(x_("vertex"), y_("vertex"))#
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#color(white)(.........................)color(green)(" Preamble")#

There are two ways of doing this.

It looks as though the fashionable way at the moment is 'completing the square' alternatively known as a 'vertex equation'.

The other, which I am going to show you, is the basis upon which completing the square is built on.
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#color(Blue)(underline(Stepcolor(white)(.)1))#

Write the given equation in the form of:
#y=2(x^2-2x+3/2)#

I have made it such that I have a part that starts with #x^2#

We now look at the part inside the brackets of #-2x#

We then do this: #-1/2xx-2=-1# ignoring the variable #x#

We have now found #color(green)(x_("vertex")=-1)....................(2)#

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#color(Blue)(underline(Stepcolor(white)(.)2))#

Substitute (2) into (1) giving:

#y_("vertex")=2(-1)^2-4(-1)+3#

#y_("vertex")=2+4+3#

#color(green)(y_("vertex")=9)#
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#color(purple)((x_("vertex"), y_("vertex")) = (-1,9))#