Final answer:
To find the equation of the parabola passing through (2, 2), (4, -8), and (-2, -14), we solve a system of equations derived from the general quadratic form. The solution gives the coefficients a = -2, b = 4, and c = 2, resulting in the parabola's equation as y = -2x² + 4x + 2.
Step-by-step explanation:
To determine the equation of the parabola that contains the points (2, 2), (4, -8), and (-2, -14), we need to solve a system of equations based on the general form of a quadratic equation, which is y = ax² + bx + c. Plugging in the points into the equation gives us a system of three equations:
- 2 = 4a + 2b + c
- -8 = 16a + 4b + c
- -14 = 4a - 2b + c
Solving this system will yield the values for a, b, and c that define the unique parabola. After solving, we get a = -2, b = 4, and c = 2. Hence, the equation of the parabola is y = -2x² + 4x + 2, which corresponds to option c) in the multiple-choice answers provided.