Finding the Equation of a Parabola

In this lesson, we will learn how to find the equation of a parabola given three points on the parabola. To accomplish this, we will use the three points provided to set up a system of linear equations in three variables. For vertical parabolas, we use the standard form y = ax² + bx +c and create our equations by substituting the given x and y values into the equation. This allows us to solve for the three unknowns: a, the coefficient of x², b the coefficient of x, and c, the constant. Once these values are determined, we can substitute them back into the standard form to find the equation of the parabola. Additionally, we may encounter horizontal parabolas, where the roles of x and y are swapped. In this case, the equation takes the form x = ay² + by + c. The process remains the same: we substitute the given x and y values into the equation to generate a system of equations and solve for a, b, and c. This results in the equation of a horizontal parabola. By the end of this lesson, you will understand how to derive the equation for both vertical and horizontal parabolas from three given points.