Final answer:
To find the equation of the parabola passing through given points, substitute the x and y values into the equation and solve for a, b, and c.
Step-by-step explanation:
To find an equation of the form y = ax² + bx + c for the parabola passing through points (3, -110), (2, -51), (4, -189), we can use the method of substitution.
Substituting the x and y values of each point into the equation, we get the following system of equations:
- 9a + 3b + c = -110
- 4a + 2b + c = -51
- 16a + 4b + c = -189
Solving this system of quadratic equations will give us the values of a, b, and c.
Using matrix methods or substitution, we find that a = 1, b = 10, and c = -200. Therefore, the equation of the parabola is y = x² + 10x - 200.