Question

How do i convert quadratic functions from standard to vertex form?

y=2x^2+12x+14

y=x^2+x+1

Answer 1

complete the square
y=2x^2+12x+14
you need the coefficient of x^2 to be 1 so divide everything by 2

y/2 = x^2 + 6 x + 7
move the constant to the left
y/2 - 7 = x^2 + 6 x
add the square of half the coef of x to both sides, in other words 3^2 or 9
y/2 + 2 = x^2 + 6 x + 9
or
y/2 + 2 = (x+3)^2
that is a parabola symmetric about the line x = -3
when x = -3
y/2 + 2 = 0
so y = - 4
so
vertex at (-3 , -4)

Answer 2

y = x^2 + 1 x + 1
y-1 = x^2 + 1 x

y-1 + 1/4 = x^2 + x + 1/4

y - 3/4 = (x+1/2)^2
vertex at (-1/2 , 3/4)