Final answer:
The correct equation of the parabola that passes through the given points is derived from a system of equations resulting in y = -2x² + 15x + 120, which corresponds to Option 3.
Step-by-step explanation:
To find the equation of a parabola that passes through the points (2, 127), (3,141), and (5,73), we can set up a system of equations in the form y = ax² + bx + c for each point, resulting in three equations:
- 127 = 4a + 2b + c
- 141 = 9a + 3b + c
- 73 = 25a + 5b + c
These equations can be rewritten into matrix form as:
| 4 2 1 | | a | | 127 |
| 9 3 1 | | b | = | 141 |
| 25 5 1 | | c | | 73 |
By solving this system of equations, we can find the values of a, b, and c.
After solving the system, we find that a = -2, b = 15, and c = 120. Therefore, the correct parabolic equation is y = -2x² + 15x + 120, which corresponds to Option 3.