To find the equation of the parabola from the given information, we first need to know that the general equation of a parabola is in the form y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
From the problem, we know that the vertex of the parabola, or the point (h, k), is (-2, 5). This means h = -2 and k = 5.
Next, we know that the parabola passes through the point (0, 9). This means that when x = 0, y = 9.
For the parabola to pass through the point, the point must satisfy the equation of the parabola. That is, when we substitute x = 0 and y = 9 in the equation of the parabola, we get a valid equation. In other words, we need to find the value of a.
Substituting h = -2, k = 5, x = 0, and y = 9 in the equation y = a(x - h)² + k, we get 9 = a(0 - -2)² + 5. This equation simplifies to 9 = a(4) + 5, which we can solve to get a = 1.
Therefore, the equation of the parabola that has the vertex at (-2, 5) and that passes through the point (0, 9) is:
y = 1(x + 2)² + 5.
But since in general, the form we use is y = a(x - h)² + k, we simplify the equation:
y = 1(x - (-2))² + 5,
further simplified to
y = 1(x - 2)² + 5.
That's the equation of the parabola.