Question

How do you determine if the vertex of  y=x²-2x-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  x2

 y=ax²+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.

a=1 so vertex is minimum.