can someone help me with this multiple choice

[rachael724]

What is the maximum value for f(x) = -3x2 + 12x - 1

a. 11
b. 12
c. 13
d. 14
e. 15
f. 16
g. 17
h. 18
i. none of these

I am not too well educated on maxium value.

 

[TchrWill]

f(x) = -3x^2 + 12x - 1

Taking the first derivitive and setting equal to 0, yields
df(x)/dx = -6x + 12 = 0 making x = -12/-6 = 2.
Therefore, the maximum value of f(x) is -3(2^2) + 12(2) - 1 = 11

 

[ting]

Find the vertex.

Could complete the square.

-3x^2 + 12x -1

Divide through by -3

=-3[(x^2 - 4x) + (1/3)]

=-3[(x - 2)^2 - (-2)^2 +(1/3)]

=-3[(x - 2)^2 - 4 +(1/3)]

=-3[(x - 2)^2 - (12/3) +(1/3)]

=-3[(x - 2)^2 - (11/3)]

=-3(x - 2)^2 + 11

What is the y coordinate of the vertex?