+164 The equation of a parabola is given.
y=34x2−6x+15
What are the coordinates of the vertex of the parabola?
+23252 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 )
