how do you know the x and y axis for the maximum point in sketching?

for example, y=-3x^2 + 5x -7

i completed the square and got -3(x-5/6)^2 + 109/12

so, i know the graph touches the y inetcept at -7, but is the x-axis of the turning point 5/6 or 3 x 5/6? and for the Y, how do you find it? i thought it was 109/12, but when i tried it online the graph looked different ( attached the online graph).