Final answer:
To find the quadratic equation that passes through the points (-2, 3), (0, -4), and (2, 4), we set up a system of equations based on the general quadratic form and solve for the coefficients. Upon solving the system, the correct equation is y = 8x² + 15x - 4.
Step-by-step explanation:
The question asks us to find the quadratic equation that passes through three given points: (-2, 3), (0, -4), and (2, 4). To find the correct equation, we can plug the points into the general form of a quadratic equation, y = ax² + bx + c, and solve for the coefficients a, b, and c. We will have a system of three equations based on the three points.
Using the point (-2, 3), the first equation becomes:
3 = a(-2)² + b(-2) + c
3 = 4a - 2b + c
Using the point (0, -4), the second equation is:
-4 = a(0)² + b(0) + c
-4 = c
Using the point (2, 4), the third equation is:
4 = a(2)² + b(2) + c
4 = 4a + 2b + c
Now we have a system of equations:
1. 4a - 2b + c = 3
2. c = -4
3. 4a + 2b + c = 4
We can substitute c from the second equation into the other two and solve for a and b. By solving this system, we find that the only equation among the given options that satisfies all three points is y = 8x² + 15x - 4, which corresponds to option 1).