The vertex form of a parabola is:
y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola and "a" is a constant that determines the shape of the parabola.
First, we can find the vertex of the parabola using the x-coordinate of the midpoint of the x-intercepts:
Midpoint of x-intercepts = (-2 + 4)/2 = 1
Therefore, the x-coordinate of the vertex is 1.
Since the parabola passes through the point (-1, -3), we can substitute these values into the vertex form to get:
-3 = a(-1 - 1)^2 + k
-3 = 4a + k
We also know that the parabola has x-intercepts at -2 and 4, which means that the parabola intersects the x-axis at these points. This tells us that the vertex is in the middle of these two points, or:
(1,0) = (-2 + 4)/2
We can plug this information into the vertex form to find the value of "a":
0 = a(1 - 1)^2 + k
0 = k
This means that the vertex is at (1,0), and the equation of the parabola is:
y = a(x - 1)^2
To find the value of "a", we can use the fact that the parabola passes through the point (-1,-3):
-3 = a(-1 - 1)^2
-3 = 16a
a = -3/16
Substituting this value of "a" into the vertex form, the equation of the parabola is:
y = -(3/16)(x - 1)^2