Final answer:
To determine the quadratic function from the points (0, 4), (-3, -8), and (2, -8), create a system of equations using the standard quadratic form y = ax² + bx + c and solve for the coefficients a, b, and c.
Step-by-step explanation:
To find the equation of a quadratic function defined by three points, we need to solve a system of equations based on the general form of a quadratic equation, which is y = ax² + bx + c. The given points are (0, 4), (-3, -8) and (2, -8). Plugging these into the quadratic equation gives us a system of three equations that can be used to find the values of a, b, and c.
The system derived from the points is:
- 4 = a(0)² + b(0) + c
- -8 = a(-3)² + b(-3) + c
- -8 = a(2)² + b(2) + c
Solving this system will yield the coefficients of the quadratic function. Since the calculations for this problem are extensive, you can use substitution or elimination methods to find a, b, and c. Once you have these coefficients, you can write the function as y = ax² + bx + c.