Question

How do you determine if the vertex of `y=x^2-2x-8` is a maximum or a minimum?

Answer 1

To determine if a quadratic equation's vertex is a max or a min,
check the coefficient of `x^2`

`y = ax^2 + bx + c`

if `a` is positive, the graph opens upward. so the vertex is a minimum

if `a` is negative, the graph opens downward. so the vertex is a maximum.

In your equation `a = 1`. We can conclude that the vertex is a minimum.