There are 2 parts to graphing a parabola:
1) Finding the vertex
You can find the #x#-value for the vertex with this formula:
#x= -b/(2a)#
For this equation, #b= -6# and #a= 3#. Then plug this #x# back into the original equation, #y=3x^2-6x-2#, to find the #y# value.
2) Finding the #x#-intercepts by plugging values for #a#, #b#, and #c# into the quadratic formula
#x= (-b+-sqrt(b^2-4ac))/(2a)#
#x= (-(-6)+- sqrt((-6)^2-4(3)(-2)))/(2*3)#
And because the first term, #3x^2#, is positive, we know that the parabola is shaped like a right-side-up cup, or a U shape.
