Completing the Square

Front

What is 'completing the square'?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q, where p and q are constants.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you complete the square for the equation x² - 4x + 4 = 20?

Back

1. Move 20 to the left: x² - 4x + 4 - 20 = 0. 2. Rewrite as (x - 2)² = 20.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What is the first step in completing the square?

Back

The first step is to ensure the coefficient of x² is 1. If it is not, divide the entire equation by the coefficient.

Front

How do you find the value to complete the square for x² - 6x?

Back

Take half of the coefficient of x (which is -6), square it (which is 9), and add it to both sides of the equation.

Front

What is the solution to the equation n² - 2n - 3 = 0 using completing the square?

Back

The solutions are n = 3 and n = -1.

Front

How do you solve k² - 12k + 23 = 0 by completing the square?

Back

1. Rewrite as (k - 6)² - 13 = 0. 2. Solve to get k = 6 ± √13.

Front

What is the result of completing the square for y² + 10y = -9?

Back

The solutions are y = -1 and y = -9.

Front

How do you rewrite x² + 6x = 5 in completed square form?

Back

Rewrite as (x + 3)² = 14.