3x^2 - 15x + k
The x coordinate of the vertex is 15 / [ 2*3] = 15 / 6 = 5/2
So....we want to solve this for k
3 (5/2)^2 - 15 (5/2) + k = 1
75/4 - 75/2 + k = 1
-75/4 + k = 1
k = 1 + 75/4 = 79/4
Here's a graph : https://www.desmos.com/calculator/ncm5rlbyq7