Given that the equation of a parabola is y^2+4y-8x+20=0
find the equation in the form (y-k)^2=4a(x-h).
y² + 4y - 8x + 20 = 0
Isolate the terms in y on the left side:
y² + 4y = 8x - 20
Multiply the coefficient of y, which is 4, by 1/2,
getting 2. Then square 2. getting 4, and add +4
to both sides:
y² + 4y + 4 = 8x - 20 + 4
Factor the left side, combine terms on the right:
(y + 2)(y + 2) = 8x - 16
Write the left side as the square of a binomial
and factor out 8 on the right:
(y + 2)² = 8(x - 2)
Write the 8 as 4*2
(y + 8)² = 4*2(x - 2)
Compare to
(y - k)² = 4*a(x - h)
So -k = +8 or k = -8
-h = -2 or h = 2
a = 2
Edwin
