For what constant $k$ is 1 the minimum value of the quadratic $3x^2 - 15x + k$ over all real values of $x$? ($x$ cannot be nonreal)
the x coordinate of the minimum = -(-15) / [ 2(3) ] = 15/6 = 5/2
the y coordinate of the minimum = 3(5/2)^2 - 15(5/2) + k
1 = 3(5/2)^2 - 15(5/2) + k
1 = 3(25/4) - 75/2 + k
1 = 75/4 - 75/2 + k
1 = -75/4 + k
1 + 75/4 = k
79/4 = k
