What is the maximum value of f(x)= -2x^2 -6x + 3 ?

We have the function:

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

We need to find the maximum value of
f(x).

First we look at the coefficient of x^2 which is
negative.

Then the fucntion has a maximum
point.

Now we will find the first derivative and determine
the zeros.

==> f'(x) = -4x - 6 =
0

==> -4x =
6

==> x = -6/4 = -3/2=
-1.5

Now we will find
f(-3/2)

==> f(-3/2) = -2(-3/2)^2 - 6(-3/2) +3 =
-18/4 + 18/2 + 3 = (-18+36 + 12)/4 = 30/4 = 15/2 =
7.5

Then, the
maximum value of the function f(x) is the point

( -1.5,
7.5)