The vertex of this parabola is at (-3 -1). When the y-value is 0 the x-value is 4. What is the coefficient of the squared term in the parabola's equation?

To find the coefficient of the squared term in the parabola's equation, we can use the vertex form of a parabola, which is (y = a(x - h)^2 + k), where ((h, k)) is the vertex. Here, the vertex is ((-3, -1)), so the equation becomes (y = a(x + 3)^2 - 1). Given that when (y = 0), (x = 4), we can substitute these values into the equation to find (a):

[0 = a(4 + 3)^2 - 1 \implies 0 = a(7^2) - 1 \implies 1 = 49a \implies a = \frac{1}{49}.]

Thus, the coefficient of the squared term is (\frac{1}{49}).