For what constant $k$ is 1 the minimum value of the quadratic $3x^2 - 15x + k$. x has to be real

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