Final answer:
To find the equation for the parabola going through (-4, 7), (6, -33), and (10, -105), use quadratic regression to solve for the values of a, b, and c in the general equation y = ax² + bx + c. Substituting the coordinates of the points into the equation yields a system of three equations, which can be solved to find the values of a, b, and c. The specific equation for the parabola is y = -x² - 10x - 6.
Step-by-step explanation:
To find the equation for the parabola that goes through the points (-4, 7), (6, -33), and (10, -105), we can use quadratic regression. Quadratic regression fits a parabolic function to a set of data points. The general form of the equation is y = ax² + bx + c. We need to find the values of a, b, and c.
Using the three given points, we can set up a system of three equations to solve for a, b, and c. Substituting the coordinates of the points into the equation, we get:
- 7 = 16a - 4b + c
- -33 = 36a + 6b + c
- -105 = 100a + 10b + c
Solving this system of equations, we find that a = -1, b = -10, and c = -6. Therefore, the equation for the parabola is y = -x² - 10x - 6.
Learn more about Quadratic regression