How can you use the values of a, b, and c to write a quadratic function in vertex form?

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

Step-by-step explanation:

We presume you're starting with ...

  y = ax^2 +bx +c

As you would with numbers, factor the first two terms:

  y = a(x^2 +b/a·x) +c

Add half the square of the x term inside and its opposite outside parentheses:

  y = a(x^2 +(b/a)x + (b/(2a))^2) + c - a(b/(2a))^2

  y = a(x +b/(2a))^2 +c -b^2/(4a)

You can combine the last two terms to a more familiar fraction:

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

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