Question

Y=x^2-6x+2 in vertex form and show work

Answer 1

The vertex form is

`Y=\mleft(x-3\mright)^2-7`

The form of the equation given is: Y=ax^2+bx+c

So, a=1, b=-6 and c=2

The vertex form is

`Y=a\mleft(x-h\mright)^2+k`

Where

`h=(-b)/(2a)\text{ , and k=f(h)}`

Then

`h=(-b)/(2a)=(-(-6))/(2\cdot1)=3`
`k=f(h)=f(3)=(3)^2-6\cdot3+2`

Then, using a,h and k:

`Y=(x-3)^3-7`