+0

The equation of a parabola is given.

0
289
1
+163

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
Sort:

#1
+17705
+1

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

19 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details