Question

How do you find the max and min of `y=-x^2+6` by completing the square?

Answer 1

"Completing the squares" is a bit unusual for the given equation:
`y=-x^2+6`
since in "completed square form" it would be:
`y = (-1)(x^2-0x+0)+6`
or
`y=(-1)(x-0)^2+6`

This is also the vertex form;
so the vertex is at `(0,6)`

Because of the `(-1)` factor we know that the parabola opens downward `rarr` the vertex is at a maximum.
As the magnitude of `x` increases the value of `y` decreases without bound.

So the maximum value is `6` and the minimum is `-oo`