Verified answer

h(x) = 1/2X^2 + X + (1/2)^2 1/2 - (1/2)^2 (add half the value of X to 1/2X^2 and take it from the 1/2)

h(x) = 1/2(X + 1)^2 +1/2 - 1/4 (convert to squared form by removing the X from equation)

h(x) = 1/2(X + 1)^2 +1/4 (simplify)

take the (k) value to the other side:

y-1/4 = 1/2(X + 1)^2

h(x) = 1/2(x+1)^2

so k = 0, a = 1/2, h = -1