What is the maximum value for  f(x) = x -­ 2x2 ­ - 1?

1 Answer
Jan 29, 2018

#(1/4,-7/8)#

Explanation:

Assuming you menat #x-2x^2-1#, we first rearrange this in the form #ax^2+bx+c#.

=>#-2x^2+x-1#

From this, we can get that #a=-2#, #b=1#, and #c=-1# Here, #a# is the coefficient of #x^2#, #b# is the coefficient of #x#, and #c# is the constant.

Now, since #a# is a negative number, this function has a maximum value.

To find the max/min value of a quadratic function, we have to find the #(h,k)#.

We also know that #h=(-b)/(2a)# (Try to see why!)

We can now find #h#.

=>#h=(-1)/(2*-2)#
=>#h=1/4#

We plug #h# into the quadratic function to get our #k#.

=>#-2(1/4)^2+1/4-1=k#

=>#-2(1/16)-3/4=k#

=>#-1/8-3/4=k#

=>#-7/8=k#

Therefore, our maximum point is #(1/4,-7/8)#