QUICK Completing the Square Review

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial. It takes the form (a + b)² = a² + 2ab + b² or (a - b)² = a² - 2ab + b².

Front

Identify the perfect square trinomial: x² + 14x + 49

Back

(x + 7)²

Front

What value of 'c' completes the square for x² - 8x + ___?

Back

16

Front

Complete the square for x² - 14x + ___.

Back

49

Front

Identify the equivalent expression for the perfect square trinomial: x² - 18x + 81

Back

(x - 9)²

Front

What is the value that completes the square for x² + 6x + ___?

Back

9

Front

How do you complete the square for a quadratic expression?

Back

To complete the square, take half of the coefficient of x, square it, and add it to the expression. This creates a perfect square trinomial.

Front

What is the formula for factoring a perfect square trinomial?

Back

(a + b)² = a² + 2ab + b² or (a - b)² = a² - 2ab + b².

Front

If x² + 10x + c is a perfect square trinomial, what is the value of c?

Back

25 (since (10/2)² = 25).

Front

What is the relationship between the coefficients in a perfect square trinomial?

Back

The middle term is twice the product of the square root of the first and last terms.