Checkpoint: Complete The Square

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, typically in the form (a + b)² = a² + 2ab + b².

Front

How do you find the value of c to make x² + 8x + c a perfect square trinomial?

Back

To find c, take half of the coefficient of x (which is 8), square it: (8/2)² = 16. Thus, c = 16.

Front

Factor the perfect square trinomial x² + 16x + 64.

Back

(x + 8)².

Front

What is the formula for completing the square?

Back

To complete the square for ax² + bx + c, rewrite it as a(x + b/2a)² - (b² - 4ac)/4a.

Front

Factor the expression x² - 4x + 4.

Back

(x - 2)².

Front

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

Back

49.

Front

Complete the square for x² + 12x + ____.

Back

x² + 12x + 36.

Front

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

Back

In a perfect square trinomial, the middle term is twice the product of the square roots of the first and last terms.

Front

How can you verify if a trinomial is a perfect square?

Back

Check if the square root of the first term and the last term are equal and if the middle term equals twice the product of these square roots.

Front

What is the first step in completing the square for x² + bx?

Back

Take half of b, square it, and add it to both sides of the equation.