Final answer:
To write the equations of the given quadratics, we can use the form ax² + bx + c = 0. We have three points: (-1,12), (1,2), (2,6). We can substitute each point into the quadratic equation and solve for the three unknown coefficients a, b, and c.
Step-by-step explanation:
To write the equations of the given quadratics, we can use the form ax² + bx + c = 0. We have three points: (-1,12), (1,2), (2,6). We can substitute each point into the quadratic equation and solve for the three unknown coefficients a, b, and c. Let's go through the steps:
Step 1: Substitute the first point (-1,12) into the quadratic equation:
12 = a*(-1)² + b*(-1) + c
Step 2: Substitute the second point (1,2) into the quadratic equation:
2 = a*(1)² + b*(1) + c
Step 3: Substitute the third point (2,6) into the quadratic equation:
6 = a*(2)² + b*(2) + c
We now have a system of three equations with three unknowns (a, b, c). We can solve this system of equations to find the values of a, b, and c, which will give us the equations of the quadratics.