Final answer:
To determine the equation of the quadratic function, we can use the given points to form a system of equations and solve them. The equation of the quadratic function is y = 2x^2 - 4x - 8.
Step-by-step explanation:
To find the equation of the quadratic function, we can use the given points to form three equations. Let's call the function y = f(x). The first equation is obtained by substituting (-2, 8) into the function: 8 = a(-2)^2 + b(-2) + c. The second equation is obtained by substituting (0, -8) into the function: -8 = a(0)^2 + b(0) + c. The third equation is obtained by substituting (3, -2) into the function: -2 = a(3)^2 + b(3) + c.
We now have a system of three equations with three variables (a, b, c). Solving this system will give us the values of a, b, and c, which we can then use to form the equation of the quadratic function.
After solving the system of equations, we find that the equation of the quadratic function is y = 2x^2 - 4x - 8.