Final answer:
The equation of the parabola with a vertex at (-1, 8) that passes through (2, -10) is y = -2(x + 1)^2 + 8.
Step-by-step explanation:
To write the equation for a parabola with a given vertex and a point it passes through, we use the vertex form of a parabola's equation, which is:
y = a(x - h)2 + k
where (h, k) is the vertex of the parabola. In this case, the vertex is (-1, 8). So the equation starts as:
y = a(x + 1)2 + 8
We need to determine the value of a. Since the parabola passes through the point (2, -10), we can substitute x with 2 and y with -10 to find a:
-10 = a(2 + 1)2 + 8
-10 = a(3)2 + 8
-10 = 9a + 8
-18 = 9a
a = -2
The value of a is -2. Thus, the equation of the parabola is:
y = -2(x + 1)2 + 8