Complete 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, making it easier to solve for x.

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 expression x² + bx?

Back

To complete the square, take half of b, square it, and add it to both sides of the equation.

Front

What is the formula to find the value to complete the square?

Back

The value to complete the square is (b/2)².

Front

If you have the equation x² + 6x = 5, what is the first step to complete the square?

Back

Move the constant to the other side: x² + 6x - 5 = 0.

Front

What do you add to both sides of the equation x² + 6x = 5 to complete the square?

Back

Add (6/2)² = 9 to both sides, resulting in x² + 6x + 9 = 14.

Front

What is the completed square form of x² + 6x = 5?

Back

(x + 3)² = 14.

Front

How do you solve for x after completing the square?

Back

Take the square root of both sides and solve for x: x + 3 = ±√14.

Front

What does the ± symbol represent in the context of completing the square?

Back

The ± symbol indicates that there are two possible solutions: one positive and one negative.

Front

What is the vertex form of a quadratic equation?

Back

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