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# how to find the turning point of a parabola?

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how to find the turning point of a parabola?

Oct 13, 2017

#1
+7599
+2

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

Oct 13, 2017

#1
+7599
+2

When the equation of the parabola is in this form:

y  =  ax2 + bx + c

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

----------

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

hectictar Oct 13, 2017