A parabola is a graph of a quadratic function. It looks like the letter "U" when graphed on a Cartesian plane (an X,Y axis). The quadratic function is ax^2+bx+c = 0, where a, b, and c are numbers called coefficients. The solution for any quadratic equation or parabola can be found by using a little algebra and the general formula for the quadratic equation, which is : x = -b ± sqrt(b^2 - 4ac) / 2a.
A graphing calculator (standard in many algebra classrooms) can solve a quadratic formula in seconds. Just plug in your coefficients to the calculator's quadratic solver.
Figure out the coefficients a, b, and c by looking at the given formula. For example, if you are asked to solve the parabola 3x^2 + 5x + 1 = 0, a is 3, b is 5, and c is 1.
Put the values from Step 1 into the quadratic formula: x = -5 ± sqrt (52 - 4(3) (1)) / 2 *3.
Work out the formula by performing the indicated operations: x = -5 ± sqrt (25 - 12) / 6 then x = -5 ± sqrt (13) / 6, which is the solution for the parabola.