y = 
x² + 4x - 14
Clear of fractions:
2y = -x² + 8x - 28
Factor -1 out of first two terms on the right:
2y = -1(x² - 8x) - 28
Change the parentheses to brackets so it can contain parentheses:
2y = -1[x² - 8x] - 28
To complete the square inside the bracket:
1. Take one-half of the coefficient of x. 
·(-8) = -4
2. Square the result. (-4)² = 16
3. Add it then subtract it in the bracket: Add + 16 - 16
2y = -1[x² - 8x + 16 - 16] - 28
Factor the first three terms inside the bracket as a perfect square:
2y = -1[(x-4)² - 16] - 28
Remove the bracket by distributing the -1 leaving the parentheses intact:
2y = -1(x-4)² + 16 - 28
Combine the terms +16 - 28 as -12
2y = -1(x-4)² - 12
Solve for y by dividing through by 2
y = (x-4)² - 6
Compare that to the standard vertex form:
y = a(x-h)² + k
We see that the vertex (h,k) is (4,-6) and from the original
equation y = x² + 4x - 14 tells us that the y-intercept
is (0,-14)
The axis of symmetry is the vertical line through the vertex, and
is therefore the vertical line whose equation is x=-4:
The point that matches the y-intercept on the other side of the
axis of symmetry is (8,-14), so we plot that point:
and we sketch in the parabola:
Edwin
