Step-by-step explanation:
The given parabolic equation is [tex]y=3x^{2} -4x+10[/tex].
The vertex of a parabola ( if it's axis is parallel to y-axis ) [tex]y=ax^{2} +bx+c[/tex] is given by [tex](\frac{-b}{2a},\frac{4ac-b^{2}}{4a})[/tex].
So, for the given parabola [tex]a=3,b=-4,c=10[/tex].
The vertex is [tex](\frac{-(-4)}{2*3},\frac{4*3*10-(-4)^{2}}{4*3})[/tex]
∴ The vertex is given by [tex](\frac{2}{3},\frac{26}{3})[/tex].
