Question

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

Answer 1

(2, 4)

Explanation:

The equation `y=ax^2+bx+c` can be modified to the standard form
`(x-alpha)^2=+-4p(y-beta)`, gviing vertex `(alpha, beta)` and parameter p for the size of the parabola.
This way, the vertex of the parabola `y=ax^2+bx+c` is `(-b/(2a), c-b^2/(4a))`. .
Here, `a=-1, b=4 and c=0`.

Of course, direct manipulation for the standard form is easier.