Lesson 11 Intro G2 Squaring binomials

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.

Front

How do you complete the square for the expression x² + 6x + ____?

Back

To complete the square, take half of the coefficient of x (which is 6), square it (3² = 9), and add it to the expression. The completed square is x² + 6x + 9.

Front

What is the missing value to complete the square for x² - 14x + ____?

Back

The missing value is 49, since (-14/2)² = 49.

Front

What is the formula to find the missing value 'c' in a perfect square trinomial?

Back

The formula is c = (b/2)², where b is the coefficient of x in the expression ax² + bx + c.

Front

Complete the square for x² + 12x + ____.

Back

The missing value is 36, since (12/2)² = 36.

Front

What is the completed square form of x² - 24x + ____?

Back

The completed square form is x² - 24x + 144, which can be factored as (x - 12)².

Front

How do you identify a perfect square trinomial?

Back

A perfect square trinomial can be identified if it can be factored into the form (a + b)² or (a - b)², and it follows the pattern a² ± 2ab + b².

Front

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

Back

In a perfect square trinomial of the form a² ± 2ab + b², the coefficient of x (2ab) is twice the product of the square roots of the first and last terms.

Front

What is the missing value 'c' for the expression x² + 26x + ____?

Back

The missing value is 169, since (26/2)² = 169.

Front

How do you derive the formula for completing the square?

Back

To derive the formula, take the quadratic expression ax² + bx + c, factor out 'a', and then manipulate the expression to form a perfect square.