Completing the Square

Front

What is 'Completing the Square'?

Back

A method used to solve quadratic equations by rewriting them in the form (x - p)² = q.

Front

What is the standard form of a quadratic equation?

Back

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

Front

How do you complete the square for the equation x² + 6x = 5?

Back

Add (6/2)² = 9 to both sides to get (x + 3)² = 14.

Front

What is a perfect square trinomial?

Back

An expression that can be factored into the square of a binomial, e.g., x² - 18x + 81 = (x - 9)².

Front

What is the first step in completing the square?

Back

Move the constant term to the other side of the equation.

Front

How do you find the value to complete the square for x² - 4x?

Back

Take half of -4, square it: (-4/2)² = 4.

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.

Front

What does the discriminant tell you about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the number of real solutions: positive (2 solutions), zero (1 solution), negative (no real solutions).

Front

How do you solve (x - 3)² = 49?

Back

Take the square root of both sides: x - 3 = ±7, so x = 10 or x = -4.

Front

What is the relationship between the roots and the coefficients of a quadratic equation?

Back

The sum of the roots is -b/a and the product of the roots is c/a.