How to Convert Quadratic Equations From Standard to Vertex Form

by Nucreisha Langdon

The standard form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are coefficiencts and y and x are variables. It is easier to solve a quadratic equation when it is in standard form because you compute the solution with a, b, and c. However, if you need to graph a quadratic function, or parabola, the process is streamlined when the equation is in vertex form. The vertex form of a quadratic equation is y = m(x-h)^2 + k.

Factor the coefficient a from the first two terms of the standard form equation and place it outside of parentheses. For instance, if you are converting 2x^2 - 28x + 10 to vertex form, you first write 2(x^2 - 14x) + 10.

Divide coefficient of the x term inside parentheses by 2, then square that number. In the example, the coefficient of x inside parentheses is -14. You compute -14/2 which equals -7, and then (-7)^2 which equals 49.

Add the number inside the parentheses, and then to balance the equation, multiply it by the factor on the outside of parentheses and subtract this number from the whole quadratic equation. For example, 2(x^2 - 14x) + 10 becomes 2(x^2 - 14x + 49) + 10 - 98, since 49*2 = 98.

Simplify the equation by combining the terms at the end. For example, 2(x^2 - 14x + 49) - 88, since 10 - 98 = -88.

Convert the terms inside parentheses to a squared unit of the form (x - h)^2. The value of h is half the coefficient of the x term. For example, 2(x^2 - 14x + 49) - 88 becomes 2(x - 7)^2 - 88. The quadratic equation is now in vertex form.

About the Author

Nucreisha Langdon has written professionally since 1991. She has ghostwritten more than 20 romantic fantasy novels, while her nonfiction work has appeared in the "Gainesville Sun" and the "Austin Chronicle." Langdon holds a Bachelor of Science in mathematics and a Bachelor of Arts in English from the University of Florida.

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