SOLUTION: Find the real number k such that f(x) = f(k - x) for all real numbers x, where f(x) = 3x^2 - 4x

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.

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) (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.

RELATED QUESTIONS
Let f(x) = 3x^2 - 4x. Find the constant k such that f(x) = f(k - x) for all real numbers... (answered by richard1234)

Let f(x) = 3x^2 - 4x. Find the constant k such that f(x) = f(k - x) for all real numbers (answered by reviewermath)

Let f(x) = 3x^2 - 4x. Find the constant k such that f(x) = f(k - x) for all real numbers (answered by ikleyn)

Let the function f be defined by y = f(x), where x and f(x) are real numbers. f(x) = 4x... (answered by richard1234,ewatrrr)

Let f(x) = x^2 - 2x. Find all real numbers x such that f(x) =... (answered by robertb,richard1234,Natolino1983)

Let f(x) = x^2 - 2x. Find all real numbers x such that f(x) =... (answered by jim_thompson5910)

f(x)=x^2+6x+20+k(x^2-3x-12) where k is real. Find value of k given that f(x) is a... (answered by math_tutor2020,greenestamps)

Let f be a function such that f(x) + f(2x + y) + 5xy = f(4x - y) - x^2 + 5xy - 8x + 17y... (answered by CPhill,ikleyn)

Find the sum of the constants a, h, and k such that 2x^2 - 8x + 7 = a(x - h)^2 + k for... (answered by josgarithmetic)