Question

What is the vertex of the graph of y=3x^2+2x+1

Answer 1

vertex = ( -
`(1)/(3)`,
`(2)/(3)`)

given a parabola in standard form : ax² + bx + c (a ≠ 0 )

then the x-coordinate of the vertex = -
`(b)/(2a)`

y = 3x² + 2x + 1 is in standard form

with a = 3, b = 2 and c = 1

`x_(vertex)` = -
`(2)/(6)` = -
`(1)/(3)`

substitute this value into the equation for y- coordinate of vertex

`y_(vertex)` = 3( -
`(1)/(3)`)² + 2(-
`(1)/(3)`) + 1

=
`(1)/(3)` -
`(2)/(3)` +
`(3)/(3)` =
`(2)/(3)`

vertex = ( -
`(1)/(3)`,
`(2)/(3)`)