ANSWER
[tex]( \frac{3}{34} , \frac{501}{34} )[/tex]
EXPLANATION
The given parabola has equation;
[tex]y = 34 {x}^{2} - 6x + 15[/tex]
Comparing this equation to
[tex]y = a{x}^{2} + bx + c[/tex]
we have
a=34, b=-6 and c=15
The x-coordinate of the vertex is given by:
[tex]x = \frac{ - b}{2a} [/tex]
[tex]x = \frac{ - - 6}{2(34)} [/tex]
[tex]x = \frac{ 6}{2(34)} [/tex]
[tex]x = \frac{ 3}{34} [/tex]
The y-coordinates of the vertex is obtained by substituting the x-value of the vertex into the equation:
[tex]y = 34( { \frac{3}{34} })^{2} - 6( \frac{3}{34}) + 15[/tex]
[tex]y = { \frac{9}{34} } - \frac{18}{34}+ 15[/tex]
[tex]y = \frac{501}{34} [/tex]
The vertex is
[tex]( \frac{3}{34} , \frac{501}{34} )[/tex]
