**Quote:**

Since it has to be the least value I've chosen the solution with "–".

The question does NOT ask to find the least value of

*x*. It asks to find such value of

*x* that

*f*(

*x*) will be the least.

**Quote:**

I have solved for *x* and I got the A solution.

A is a trap choice. Apparently you solved 0 =

*x*² + 2

*bx* + 4, which corresponds to

*f*(

*x*) = 0.

**But, why must the least value of ***f*(*x*) be 0? There are no logical grounds for that.

The least value of

*f*(

*x*) can also be positive or negative depending on the value of

*b*. Pick some values for

*b* between -2 and 2. Then pick some values for

*b* greater than 2. You'll see that the least value of

*f*(

*x*), which is (4 – b²), will have a different sign.

Furthermore, choice A can NOT be applied if

*b* is between -2 and 2, while question statement asks "for any

*b*". That is a hint that choice A is NOT a correct one.

Here is the image of general view of such parabolas that a quadratic function can be. Take a look at their bottom points that correspond to the least value for each parabola. Such point can be below the

*x*-axis (negative), above the

*x*-axis (positive) or lie on the

*x*-axis (zero).