Hi,

We have to write the equation in the vertex form:

-2x² + 12x - 13 = -2( x² - 6x ) - 13 

= -2( x² - 2*3x + 3² - 3²) - 13

= -2( (x-3)² - 3² ) -13

= -2( (x-3)² - 9) -13

=-2(x-3)² + 18 - 13

=-2(x-3)² + 5

then the equation of the parabola in vertex form is y = -2(x+3)² + 5

thus the vertex of the parabola is ( 3 , 5 )

regards.

SAID