Question

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

Answer 1

`(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)`