Asapdetermine the value of k in y=-x^2+4x +k that will result in the intersection of the line y=8x--2 with the quadratic at a) two points b) one point c) no points

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