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The equation of a parabola is given.

 

y=34x2−6x+15

 

What are the coordinates of the vertex of the parabola?

Gwendolynkristine  May 11, 2017
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Equation:  y  =  34x2 - 6x + 15

Remove the constant term (15) from the right side by subtracting 15 from both sides:

             y - 15  =  34x2 - 6x

Factor out 34 from the right side:

            y - 15  =  34( x2 - 6/34x  )

Simplify:

           y - 15  =  34( x2 - 3/17x  )

Complete the square on the right side:

   --  First, divide the coefficient of the x-term by 2:   (-3/17) / 2  =  -3/34

   --  Second, square this result:  (-3/34)2  =  9/1156

Introduce this term into the right side:

          y - 15  =  34( x2 - 3/17x + 9/1156 )

But, you now have to make a corresponding change to the left side; you have added the term 34(9/1156) = 9/34 on the right side so you must now add it to the left side:

          y - 15 + 9/34  =  34( x2 - 3/17x + 9/1156 )

Simplify the left side and factor the right side:

         y - 501/34  =  34( x - 3/34 )2

The vertex will be the point ( 3/34, 501/34 )

geno3141  May 11, 2017

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