Final answer:
To find the quadratic equation that fits the given set of data points, set up a system of equations using the coordinates of each point and solve for the values of a, b, and c. Substitute these values back into the general form of a quadratic equation to obtain the equation that fits the data points.
Step-by-step explanation:
To find the quadratic equation that fits the given set of data points (-4,-7),(2,29),(-5,-6), we can use the general form of a quadratic equation, y = ax² + bx + c. By substituting the coordinates of each point into the equation, we can set up a system of equations to find the values of a, b, and c. Solving the system will give us the quadratic equation that fits the given data points.
Using the given points (-4,-7), (2,29), and (-5,-6), we can set up the following system of equations:
-7 = 16a - 4b + c,
29 = 4a + 2b + c,
-6 = 25a - 5b + c.
Solving this system of equations will give us the values of a, b, and c, which we can then substitute back into the general form of a quadratic equation to obtain the equation that fits the given data points.