What is an equation of a parabola with vertex at the origin and focus (0, 7)

a. y = - 1/28 x^2

b. y = 1/28 x^2

c. x = - 1/28 y^2

d. x = 1/28 y^2

Answer: B) y = (1/28) x^2

Explanation:

p = focal distance = 7

the focal distance is from the vertex to the focus

The parabola opens upward (since the vertex is below the focus) so 'a' is positive and a = 1 / (4p) = 1 / (4*7) = 1/28

The vertex is (h, k) = (0,0)

Put this all together into the formula below and simplify

y = a (x-h) ^2 + k

y = (1/28) (x - 0) ^2 + 0

y = (1/28) x^2