Question

When you change a standard form into a vertex form, a number is added and subtracted as part of a process. e.g. (x² + 6x + 9 - 9) -4. Explain why this process is called "completing the square.

Option 1: It makes the expression inside the parentheses a perfect square trinomial, which simplifies the equation and helps identify the vertex of the parabola.

Option 2: By adding and subtracting the same value, we create a square, symbolizing the completion of a square in the quadratic equation.

Option 3: This method transforms the quadratic expression into a fully squared form, like a puzzle piece fitting perfectly, hence "completing" the square.

Option 4: Adding and subtracting the square of half the coefficient of 'x' not only makes the equation easier to work with but also resembles a geometric square, hence the name "completing the square.

Answer 1

Completing the square is the process of changing a standard form quadratic equation into vertex form by making the expression a perfect square trinomial. It simplifies the equation and helps identify the vertex of the parabola.

Step-by-step explanation:

The process of changing a standard form quadratic equation into vertex form is called 'completing the square' because it involves making the expression inside the parentheses a perfect square trinomial. Option 1 is the correct explanation because completing the square simplifies the equation and helps identify the vertex of the parabola. By adding and subtracting the same value, we create a square, symbolizing the completion of a square in the quadratic equation.