Final answer:
Using the given points to create a system of equations based on the form y = ax^2 + bx + c, we find that the coefficients a = -1, b = 6, and c = -11, giving us the quadratic equation y = -x^2 + 6x - 11. However, this solution is not offered in the provided answer options, suggesting an error in the question or options provided.
Step-by-step explanation:
To find the equation of a quadratic that passes through the points (1, -6), (2, 3), and (5, -6), we assume a general form of y = ax^2 + bx + c. We will substitute the given points into this equation to get a system of equations to solve for the coefficients a, b, and c.
- Substituting (1, -6): -6 = a(1)^2 + b(1) + c
- Substituting (2, 3): 3 = a(2)^2 + b(2) + c
- Substituting (5, -6): -6 = a(5)^2 + b(5) + c
Solving the system of equations, we get:
- -6 = a + b + c
- 3 = 4a + 2b + c
- -6 = 25a + 5b + c
This can be solved using methods such as substitution or elimination. Upon solving, we find that a = -1, b = 6, and c = -11. Therefore, the quadratic equation is y = -x^2 + 6x - 11, which is not listed in the provided options, indicating a possible mistake in the question or the options.