Write an equation for a parabola that opens upward from its vertex at (-4,3). What is the equation of its line of symmetry?

To write the equation of a parabola that opens upward from its vertex, we can use the general form of a parabolic equation, which is given by:

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

Where (h, k) represents the vertex coordinates of the parabola. In this case, the vertex is (-4,3), so we have h = -4 and k = 3. Plugging these values into the equation, we get:

y = a(x - (-4))^2 + 3
y = a(x + 4)^2 + 3

Now, to find the equation of the line of symmetry, we know that the line of symmetry always passes through the vertex of the parabola. Therefore, the equation of the line of symmetry in this case is simply x = -4.

So, the equation of the parabola is y = a(x + 4)^2 + 3, and the equation of its line of symmetry is x = -4.