Final answer:
To find the equation of the parabola that passes through the points (-2,-3), (2,9), and (6,5), we assume the general form y = ax^2 + bx + c and plug in the points to get a system of equations. By solving for a, b, and c, we can determine the parabola's equation.
Step-by-step explanation:
To find the equation of the parabola that passes through the points (-2,-3), (2,9), and (6,5), we can assume the equation of the parabola is in the form y = ax² + bx + c. We need to solve for the coefficients a, b, and c using the given points, by substituting the x and y values from each point into the equation to create a system of three equations:
- Using point (-2, -3): (-3) = a(-2)² + b(-2) + c
- Using point (2, 9): 9 = a(2)² + b(2) + c
- Using point (6, 5): 5 = a(6)² + b(6) + c
This results in:
- 4a - 2b + c = -3
- 4a + 2b + c = 9
- 36a + 6b + c = 5
We then solve this system of equations to find the values of a, b, and c. Once we have these values, we will have the parabola's equation.