Answer:
C.) The only extreme point is (-1, 18).
Step-by-step explanation:
You want the local and global extrema of f(x) = -2x² - 4x + 16.
Extreme points
Unless the domain is restricted to a particular interval, the extrema of a polynomial function will be its turning points. The number of possible turning points is 1 less than the degree of the equation.
An even-degree polynomial equation will always have at least one global extreme on the domain of all real numbers.
The given 2nd-degree equation will have exactly one extreme point: its vertex at (-1, 18).
__
Additional comment
The vertex of ax² +bx +c is located at x=-b/(2a). Here, that is x=-(-4)/(2(-2)) = -1. The value of f(-1) is -2 -(-4) +16 = 18, so the extreme point is (-1, 18). A graphing calculator finds it quickly.
