The standard form of the equation of a parabola is y = x2 - 6x 14. what is the vertex form of the equation?

  y = x^2 - 6x+14
First, group:
y=(x^2-6x)+14
y=(x^2-6x+)+14-

Second, add placeholders:

Notice that the second blank is subtracted to account for what you're adding to complete the square. 

Take the coefficient of the x term: -6 
Divide it by 2: -6 / 2 = -3 
Square it: (-3)² = 9 

Add 9 to both blanks.
y=(x^2-6x+9)+14-9
x² - 6x + 9 is the expanded form of a perfect square binomial. 

Remember that (a - b)² = a² - 2ab + b². Apply this to what you have. 

y=(x^2-6x+9)+14-9
y=(x-3)^2+14-9

Now, simplify:
y=(x-30^2+5