Respuesta :

Answer:

16y = (x - 4)² + 32

Step-by-step explanation:

y = a(x - h)² + k

(h,k) = (4,2)

y = a(x-4)² + 2

When x = 0, y = 3

3 = a(0-4)² + 2

3 - 2 = 16a

16a = 1

a = 1/16

y = (1/16)(x - 4)² + 2

Multiplying the equation by 16:

16y = (x - 4)² + 32

The standard form is (x - h)2 = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y - k)2 = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p.