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  ( - \(\frac{2}{3}\),  - \(\frac{1}{3}\) )