The first thing we must do in this case is to equal both functions:
-x ^ 2 + 4x + k = 8x-2
We rewrite the function:
-x ^ 2 + 4x + k - 8x + 2 = 0
-x ^ 2 -4x + (k + 2) = 0
We use the resolver:
x = (- b +/- root (b ^ 2 - 4 * a * c)) / 2 * a
x = (- (- 4) +/- root ((- 4) ^ 2 - 4 * (- 1) * (k + 2))) / 2 * (- 1)
x = (4 +/- root (16 + 4 * (1) * (k + 2))) / - 2
a) two points
16 + 4 * (1) * (k + 2)> 0
(k + 2)> -16/4
(k + 2)> -4
k> -4 -2
k> -6
b) one point
16 + 4 * (1) * (k + 2) = 0
(k + 2) = -16/4
(k + 2) = -4
k = -4 -2
k = -6
c) no points
16 + 4 * (1) * (k + 2) <0
(k + 2) <-16/4
(k + 2) <-4
k <-4 -2
k <-6
