How to Solve a Parabola

By Stephanie Ellen; Updated April 24, 2017

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.

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.


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.

About the Author

Stephanie Ellen teaches mathematics and statistics at the university and college level. She coauthored a statistics textbook published by Houghton-Mifflin. She has been writing professionally since 2008. Ellen holds a Bachelor of Science in health science from State University New York, a master's degree in math education from Jacksonville University and a Master of Arts in creative writing from National University.