Answer:
(x) = (-19/9)(x + 3)^2 + 5
Step-by-step explanation:f(x) = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola. Given that the vertex is (-3, 5), we can plug in these values into the vertex form equation:
f(x) = a(x - (-3))^2 + 5
which simplifies to:
f(x) = a(x + 3)^2 + 5
Now, we know that the function passes through the point (0, -14). We can plug in these values into the equation and solve for 'a':
-14 = a(0 + 3)^2 + 5
-14 = 9a + 5
Subtracting 5 from both sides:
-19 = 9a
Dividing both sides by 9:
a = -19/9