To find the x-intercepts of a function set f(x) (or y) to zero. If you think about it graphically, the x-intercepts occur when your graph hits the x-axis, and the x-axis is the line y=0.
Now the equation looks like this: 0 = -3x2+7x+12
and you can use quadratic formula to find the x-values
x = [-7 +/- √(72-4(-3)(12)) ] / [(2)(-3)]
x = [ -7 +/- √(49 +144) ] / -6
x = [-7 +/- √(193)] / -6
the vertex of your graph will fall in the middle of your x-intercepts, so if you take the average of your intercepts, that will be the x-value of your vertex, then you can plug that back into your function to solve for the y-value of the vertex