Question

How do you find the vertex of `y = x^2 - 4x + 4`?

Answer 1

`(2,0)`

Explanation:

Method 1:
`y=x^2-4x+4`
complete the square to get:
`y=(x-2)^2`

pick out the x value (2), and the y value (o)
to get:
`(2,0)`

method 2:
`y=x^2-4x+4`
`\frac{dy}{dx} = 2x-4`
let `\frac{dy}{dx}=0` as the vertex is when the gradient of the curve is 0.

to get `x = 2`
substitute that into the original equation to get `(2,0)`