Question

How do you find the vertex of a parabola given by the equation `x = y^2 - 4y + 3`?

Answer 1

`"vertex "=(-1,2)`

Explanation:

`"since the equation has a "y^2" term this indicates a"`
`"horizontal opening parabola with equation"`

`(y-k)^2=4a(x-h)`

`"where "(h,k)" are the coordinates of the vertex"`

`"to obtain this form "color(blue)"complete the square"`

`x=(y-2)^2-4+3`

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

`"with "h=-1" and "k=2`

`color(magenta)"vertex "=(-1,2)`
graph{x=y^2-4y+3 [-10, 10, -5, 5]}