Question

Using the completing-the-square method, find the vertex of the function f(x) = –2x2 + 12x + 5 and indicate whether it is a minimum or a maximum and at what point.. .

Answer 1

F ( x ) = - 2 x² + 12 x + 5 = - 2 ( x² - 6 x ) + 5 = - 2 ( x² - 6 x + 9 - 9 ) + 5 =
- 2 ( x² - 6 x + 9 ) + 18 + 5 = - 2 ( x - 3 )² + 23 
f ( x ) = a ( x - k )² + h ( the vertex form ), k = 3, h = 23. 
a = - 2 < 0, that means the vertex coordinates ( 3, 23 ) represents a maximum.