Question

How do you write `F(x)=x^2-2x+5` in vertex form?

Answer 1

`y=(x-1)^2+4`

Explanation:

Given -

`F(x)=x^2-2x+5`

`y=x^2-2x+5`

Vertex

x - coordinate of the vertex

`x=(-b)/(2a)=(-(-2))/(2 xx 1)=2/2=1`

y - coordinate

`y=(1)^2-2(1)+5=1-2+5=4`

Vertex `(1,4)`

Parabola in vertex form

`y=a(x-h)^2+k`

Where -

`a=1` ----- coefficient of `x^2`
`h=1` --- x - coordinate of the vertex
`k=4` --- y - coordinate of the vertex

Substitute these values into the equation.

`y=1(x-1)^2+4`
`y=(x-1)^2+4`
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