Does the function have a minimum or maxium value ? What is the function minuim or maximum ? Where does the minimum or maxium value occur ? g(x)=-3x^-6x-6

Question

This question is bugging me !!!! I can't even do this . I tried the calculator , I just can't get it . 

Answer 1

Do you mean g(x)=-3x^2-6x-6? If so, then you got an equation of a parabola. Since the coefficient of the x^2 term is negative, the function opens down. Hence, the function has one maximum value in which is its vertex.

 

To determine the vertex, you could use completing the square in rewriting the equation in the form of g(x) = (     )^2 + constant.

 

The first step is factor out -3 from the first two terms of the equation in which is:

 

g(x)=-3(x^2+2x)-6

 

Next, add a term within the parenthesis to make it a perfect square in which is:

 

g(x)=-3(x^2+2x+1)-6+3*1 Note: the last term 3*1 is added to make the overall equation equivalent to the original equation.

 

Simplify and evaluating the last two terms in which is:

 

g(x)=-3(x+1)^2-3 Therefore, the vertex occurs at (-1,-3).