Enter the coefficients of your quadratic equation into the calculator to determine the completed square form.
Square Completion Formula
The following formula is used to complete the square for a quadratic equation.
a(x + h)^2 + k
Variables:
- a is the coefficient of the quadratic term.
- h is calculated as $h = -\frac{b}{2a}$.
- k is calculated as $k = c – \frac{b^2}{4a}$.
To complete the square, use the formula and substitute the values of a, b, and c.
What is Completing the Square?
Completing the square is a method used to solve quadratic equations and to convert the standard form of a quadratic equation into vertex form. This involves creating a perfect square trinomial from a quadratic expression, making it easier to solve or analyze the equation.
How to Complete the Square?
The following steps outline how to complete the square using the given formula.
- First, write the quadratic equation in the form $ax^2 + bx + c$.
- Next, determine the coefficients a, b, and c from the equation.
- Calculate h using the formula $h = -\frac{b}{2a}$.
- Calculate k using the formula $k = c – \frac{b^2}{4a}$.
- Write the completed square form as $a(x + h)^2 +