Question 1209318
.
Find the real number k such that f(x) = f(k - x) for all real numbers x, 
where f(x) = 3x^2 - 4x - 2x^2 + 19x.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
The reduced quadratic polynomial is

    f(x) = x^2 + 15x.


They ask where to place a mirror (position "k") to reflect parts of the parabola 
one onto another.


Obviously, the mirror should be the axis of symmetry through the vertex, 
which is half-way between the roots  x= 0  and  x= -15.


So, the position of the mirror is k = -15/2 = -7.5.


<U>ANSWER</U>.  k = -7.5.
</pre>

Solved.