Find the minimum or maximum of the quadratic function:
A) Maximum: 18
B) Maximum: -6
C) Minimum: -14
D) Minimum: 4
E) Minimum: 14

Question

Find the minimum or maximum of the quadratic function: 
A) Maximum: 18 
B) Maximum: -6 
C) Minimum: -14 
D) Minimum: 4 
E) Minimum: 14

Quizplus · Accepted Answer

Since the coefficient of the squared term is positive, the graph of the quadratic function is a parabola opening upwards. The vertex of this parabola represents the minimum value of the function. 
Using the formula to find the vertex:
x = -b/2a = -(9)/(2(1)) = -9/2 
f(-9/2) = 2(-9/2)^2 - 9(-9/2) - 16 
= 2(81/4) + 81/2 - 16 
=  162/4 + 162/4 - 64/4 
=  (162 + 162 - 64)/4 
=  260/4 
=  65 
Therefore, the minimum value of the quadratic function is -14, and the answer is choice C.

Find the Minimum or Maximum of the Quadratic Function