When graphed which equation will yield the same maximum as the graph of y=-3x+6x+9a) y=-3(x-1)^2+12b) y=3(x+1)^2-12c) y=3(x-1)^2-12d) y=3(x+1)^2+12

The given function ⇒⇒⇒ y = -3x² + 6x + 9
It has a max value at x= 1   y = -3*(1)² + 6 * 1 + 9 = 12
see the attached figure 1 ⇒⇒⇒ The given function in blue graph
graphing the options to find which function has maximum as the given function. see the attached figure (2)

a) y=-3(x-1)²+12  ⇒⇒⇒ Black graph ⇒⇒⇒ maximum = 12

b) y=3(x+1)²-12   ⇒⇒⇒ Red graph   ⇒⇒⇒ minimum = -12

c) y=3(x-1)²-12    ⇒⇒⇒ Green graph ⇒⇒⇒ minimum = -12

d) y=3(x+1)²+12  ⇒⇒⇒ Gray graph   ⇒⇒⇒ minimum = 12

By comparing the results obtained 
∴ The equation which has the maximum as the graph of y=-3x²+6x+9

is option (a). y=-3(x-1)²+12