Using the completing-the-square method, find the vertex of the function f(x) = –2x^2 + 12x + 5 and indicate whether it is a minimum or a maximum and at what point.

a. maximum at (–3, 5)

b. minimum at (–3, 5)

c. maximum at (3, 23)

d. minimum at (3, 23)

Option C. Maximum at  

Step-by-step explanation:

we have

Completing the square

--------> quadratic equation in vertex form

The vertex is the point

This is a vertical parabola open downward

therefore

The vertex is a maximum

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.