Question
A parabola has a vertex (4,2) and
contains the point (-2,26). what is the equation of the parabola?
Answers
Damon
(x-4)^2 = k (y-2)
x^2 - 8 x + 16 = k y - 2 k
put in (-2,26)
4 + 16 + 16 = k(26) -k(2)
36 = 24 k
k = 36/24 = 3/2
so
x^2 - 8 x + 16 = 3/2 y - 3
2 x^2 -16 x + 32 = 3 y -6
3 y = 2 x^2-16 x + 38
y = (2/3) x^2 -(16/30 x + 38/3
x^2 - 8 x + 16 = k y - 2 k
put in (-2,26)
4 + 16 + 16 = k(26) -k(2)
36 = 24 k
k = 36/24 = 3/2
so
x^2 - 8 x + 16 = 3/2 y - 3
2 x^2 -16 x + 32 = 3 y -6
3 y = 2 x^2-16 x + 38
y = (2/3) x^2 -(16/30 x + 38/3