SOLUTION: 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.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 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.      Log On


   

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.
Answer by ikleyn(52898) About Me  (Show Source):
You can put this solution on YOUR website!
.
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.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

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.


ANSWER.  k = -7.5.

Solved.