This DE has characteristic equation

with a repeated root at r = 3/2. Then the characteristic solution is

which has derivative

Use the given initial conditions to solve for the constants:


and so the particular solution to the IVP is

The answer you're looking for will be,
ANSWER: 3x(x + 2)(x - 2)
You're welcome.
STEPS:
#1. Factor out common term 3x.
The vertex is (-1, 2).
The equation of parabola:
where (h, k) is the vertex
We have h = -1 and k = 2.
Substitute:

Answer:
the 4th one ,hoped this help