How Do You Write Standard-Form Equations for Parabolas?

The standard form of a quadratic equation is y = ax^2 + bx + c, so you may need to move terms around to make the equation take this form. A quadratic equation might be written in the vertex form, which is y = a(x - h)^2) + k. The vertex form of the equation makes it easy to look at the h and k variables and find the vertex of the parabola.

If the equation is written in the vertex form, first expand the binomial using the FOIL method: multiplying the first terms, outside terms, inside terms and last terms. The expression (x - h)^2 is rewritten as (x - h)(x - h). For example, assume the equation is 2(x - 1)^2 + 3. It is written as 2(x - 1)(x - 1) + 3. The two terms convert to x^2 - 2x + 1. Multiplying it by 2 makes it 2x^2 - 4x + 2, and the 3 is added. Therefore, the final equation is y = 2x^2 - 4x + 5. It is now in standard form. The vertex form is easier to start working with, but some math problems may require the student to find the standard formula.