SOLUTION: Find the value/s of k so that the minimum value of f(x) = x^2 + kx + 3 is the same as the maximum value of g(x) = k + 4x - x2.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the value/s of k so that the minimum value of f(x) = x^2 + kx + 3 is the same as the maximum value of g(x) = k + 4x - x2.      Log On


   

Question 1002046: Find the value/s of k so that the minimum value of f(x) = x^2 + kx + 3 is the same as the maximum value of g(x) = k + 4x - x2.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Vertices must be equal and this means that f%28x%29-g%28x%29=0 JUST FOR THE difference at this common vertex.

x%5E2%2Bkx%2B3-%28-x%5E2%2B4x%2Bk%29=0
x%5E2%2Bkx%2B3%2Bx%5E2-4x-k=0
2x%5E2%2Bkx-4x%2B3-k=0
highlight_green%282x%5E2%2B%28k-4%29x%2B%283-k%29=0%29

Still a quadratic equation with variables x and k. This equation will have ONE solution or zero, IF the discriminant is zero. The discriminant expression will involve k but NOT x.

Discriminant: %28k-4%29%5E2-4%2A2%2A%283-k%29=0------Solve for k.