Respuesta :
Answer:
vertex = ( [tex]\frac{2}{3}[/tex], [tex]\frac{8}{3}[/tex] )
Step-by-step explanation:
given the equation of a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = 3x² - 4x + 3 ← is in standard form
with a = 3 , b = - 4 , then
x = - [tex]\frac{-4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
substitute x = [tex]\frac{2}{3}[/tex] into the equation for corresponding y- coordinate of vertex
y = 3([tex]\frac{2}{3}[/tex] )² - 4([tex]\frac{2}{3}[/tex] ) + 3
= 3([tex]\frac{4}{9}[/tex] ) - [tex]\frac{8}{3}[/tex] + 3
= [tex]\frac{4}{3}[/tex] - [tex]\frac{8}{3}[/tex] + [tex]\frac{12}{3}[/tex]
= [tex]\frac{8}{3}[/tex]
vertex = ( [tex]\frac{2}{3}[/tex], [tex]\frac{8}{3}[/tex] )
