how to find the turning point of a parabola?

When the equation of the parabola is in this form:

y  =  ax² + bx + c

The  x-coordinate  of the turning point   =   - $\frac{b}{2a}$

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For example, if the equation of the parabola is

y  =  3x² + 4x + 1

The  x-coordinate  of the turning point   =   - $\frac{4}{2(3)}$   =   - $\frac{2}{3}$

Plug this in for  x  to find the value of the  y-coordinate.

y   =   3( - $\frac{2}{3}$ )² + 4( - $\frac{2}{3}$ ) + 1   =   - $\frac13$

So the turning point is  ( - $\frac{2}{3}$,  - $\frac{1}{3}$ )