I apologize for the error in my previous response. Here's a revised solution:
The parabola can be written in the standard form:
y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.
Since the x-intercepts are (-10,0) and (-2,0), we can write the equation in factored form as:
y = a(x + 10)(x + 2)
Expanding this expression, we get:
y = ax^2 + 12ax + 20a
Since the y-intercept is at (0,-4), we know that:
-4 = 20a
Therefore, a = -1/5. Substituting this into the equation, we get:
y = (-1/5)x^2 - (12/5)x - 8
The vertex of this parabola can be found using the formula:
h = -b/(2a) and k = f(h)
where b = -12/5 is the coefficient of the x term.
Plugging in the values of a, b, and f(x) = (-1/5)x^2 - (12/5)x - 8, we get:
h = -(-12/5)/(2*(-1/5)) = 6
k = (-1/5)(6)^2 - (12/5)(6) - 8 = -44
Therefore, the equation of the parabola is:
y = (-1/5)(x - 6)^2 - 44
I apologize again for the confusion caused by my earlier response.