Final answer:
To determine the equation of the parabola, plug the given points into the general quadratic equation y = ax² + bx + c, creating a system of equations. Solve the system for a, b, and c to find the coefficients that describe the parabola representing the dependence of y on x.
Step-by-step explanation:
To find the equation of the parabola that fits the given points x=[-1,1,3,5] and y=[-14,14,-14,-98], one approach is to set up a system of equations using the general form of a quadratic function, which is y = ax² + bx + c. Plugging in the x and y values from the points into this equation, we create a system of equations that can be solved for the coefficients a, b, and c. This system will have three equations, as we need at least three points to define a parabola.
Let's plug in the points into the quadratic equation:
- For x=-1 and y=-14: (-14) = a(-1)² + b(-1) + c
- For x=1 and y=14: (14) = a(1)² + b(1) + c
- For x=3 and y=-14: (-14) = a(3)² + b(3) + c
- For x=5 and y=-98: (-98) = a(5)² + b(5) + c
Solving this system of equations will yield the values of a, b, and c, which gives us the specific quadratic formula that describes the dependence of y on x. Note that this assumes the points do indeed fall on a parabola; outliers or mistakes in data collection can affect the outcome.
Keep in mind that due to the complexity of solving a system of equations here, the use of algebraic methods or matrix operations might be required, which is usually covered in high school algebra or pre-calculus courses.