Final answer:
To determine the equation of a parabola that passes through the points (5,210), (1,14), and (-3,10), the coefficients a, b, and c of the equation y = ax² + bx + c can be found by solving a system of equations derived from these points.
Step-by-step explanation:
To find the equation of a parabola using quadratic regression that goes through the points (5,210), (1,14), and (-3,10), you typically use a statistical calculator or software that can perform regression analysis. However, as you've provided only three points, they will define a unique parabola without the need for regression. Instead, we can solve a system of equations to find the coefficients a, b, and c such that the equation y = ax² + bx + c fits the points exactly.
The system of equations based on the given points is:
- 210 = a(5)² + b(5) + c
- 14 = a(1)² + b(1) + c
- 10 = a(-3)² + b(-3) + c
By solving this system, we can find the values of a, b, and c, which will yield the equation of the parabola that goes through the three points.