vertex = ( - [tex]\frac{1}{3}[/tex], [tex]\frac{2}{3}[/tex])
given a parabola in standard form : ax² + bx + c (a ≠ 0 )
then the x-coordinate of the vertex = - [tex]\frac{b}{2a}[/tex]
y = 3x² + 2x + 1 is in standard form
with a = 3, b = 2 and c = 1
[tex]x_{vertex}[/tex] = - [tex]\frac{2}{6}[/tex] = - [tex]\frac{1}{3}[/tex]
substitute this value into the equation for y- coordinate of vertex
[tex]y_{vertex}[/tex] = 3( - [tex]\frac{1}{3}[/tex])² + 2(- [tex]\frac{1}{3}[/tex]) + 1
= [tex]\frac{1}{3}[/tex] - [tex]\frac{2}{3}[/tex] + [tex]\frac{3}{3}[/tex] = [tex]\frac{2}{3}[/tex]
vertex = ( - [tex]\frac{1}{3}[/tex], [tex]\frac{2}{3}[/tex])
