Final answer:
To find the equation of a parabola passing through points (-5,3), (1,-3), and (2, -18), the constants a, b, and c in the quadratic equation y = ax² + bx + c must be solved for using the given points as a system of three equations.
Step-by-step explanation:
The student is asking to find the equation of a parabola that passes through three given points. We are looking for an equation in the standard quadratic form y = ax² + bx + c, where a, b, and c are constants that we need to determine. To solve for these constants, we use each of the given points as a system of three equations:
- 3 = a(-5)² + b(-5) + c
- -3 = a(1)² + b(1) + c
- -18 = a(2)² + b(2) + c
This system can be simplified to:
- 3 = 25a - 5b + c
- -3 = a + b + c
- -18 = 4a + 2b + c
By solving this system of equations, we can find the values of a, b, and c to complete the parabola equation.