Final answer:
To write a quadratic function with given characteristics, substitute the points into the quadratic equation and solve the system of equations.
Step-by-step explanation:
A quadratic function can be written in the form of f(x) = ax^2 + bx + c. To find the values of a, b, and c, we can use the given points (-3, -4), (3, 14), and (0, -4).
Substituting the x and y values of each point into the quadratic function, we get the following system of equations:
-4 = 9a - 3b + c
14 = 9a + 3b + c
-4 = c
Solving this system of equations, we find that a = 1, b = 2, and c = -4. Therefore, the quadratic function with the given characteristics is f(x) = x^2 + 2x - 4.