Can you convert a quadratic function to vertex form with the quadratic formula

Can you convert a quadratic function to vertex form with the quadratic formula or do you have to complete the square?

How do you do this?

For example, can you convert y = x^2 - 5x - 9 to vertex form with the quadratic formula?

Please show your work. 10 points to the best answer.

You can't use the quadratic formula to obtain the vertex form.
However, you can derive how to get the vertex form from the quadratic equation.

Take your general quadratic equation.

y = ax^2 + bx + c

Complete the square.

y = a(x^2 + [b/a]x) + c
y = a(x^2 + [b/a]x + [b^2/(4a^2)]) + c - b^2/(4a)
y = a(x + b/(2a))^2 + (4ac - b^2)/(4a)

The vertex form is
y = a(x - h)^2 + k

Which means you can obtain h and k easily.

h = -b/(2a)
k = (4ac - b^2)/(4a)

y = x^2 - 5x - 9
= x^2 -5x + (-5/2)^2 -9 - (-5/2)^2
= (x -5/2)^2 -9 - 25/4
= (x -5/2)^2 - 36/4 - 25/4
= ( x -5/2)^2 - 61/4