Question

Find the vertex of the parabola:

Answer 1

\[y=3x ^{2}+2x-1\]

Answer 2

dy/dx = 6x + 2

At the vertex, dy/dx = 0
Therefore, 6x+2 = 0
Therefore, x = -1/3

Find the corresponding value of y by substituting this x in the equation of parabola.

The point (x,y) would be the required vertex

Answer 3

if this is not a calculus course, (and i suspect that it is not) you can find the vertex of \(y=ax^2+bx+c\) by using the following:
the first coordinate of the vertex is \(-\frac{b}{2a}\)
in your case it is \(-\frac{2}{2\times 3}=-\frac{1}{3}\)

Answer 4

the second coordinate of the vertex is what you get when you replace \(x\) by \(-\frac{1}{3}\)

Answer 5

if you do it carefully you should find that the vertex is
\[(-\frac{1}{3},-\frac{4}{3})\]

Answer 6

Thanks so much! @satellite73