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
