Finding the Equation of a Parabola

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In this lesson, we will learn how to find the equation of a parabola given three points on the parabola. To perform this action, we will use the three points given to set up a system of linear equations in three variables. To obtain our three equations, we will simply plug in for x and y in the equation y = ax2 + bx + c. This will allow us to solve for the three unknowns: a, b, and c. Once we have solved for a, b, and c, we can plug into the standard form of a parabola: y = ax2 + bx + c and obtain our equation.
Finding the Equation of a Parabola:
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