To convert a quadratic from y = ax2 + bx + c form to vertex form, y = a (x - h) 2 + k, you use the process of completing the square. Let's see an example. Convert y = 2x2 - 4x + 5 into vertex form, and state the vertex.

Since we will be completing the square we need to isolate the x

y-5 = 2x^2 - 4x

now we the coefficient of the x^2 to equal 1 so we take 2 as common factor

y-5 = 2 (x^2 - 2x)

now we'll make it perfect square by adding 2 to both sides

y-5+2=2 (x^2-2x+1)

now simplify and convert the right side to squared expression

y-3 = 2 (x-1) ^2

now isolate the y

y = 2 (x-1) ^2 + 3 that's it