Complete the Square

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, typically in the form (a + b)² = a² + 2ab + b².

Front

How do you find the value of c in the trinomial x² + bx + c to make it a perfect square?

Back

To find c, take half of b, square it, and that value becomes c. For example, if b = 8, then c = (8/2)² = 16.

Front

What is the formula to complete the square for the expression x² + bx?

Back

The formula is x² + bx = (x + b/2)² - (b/2)².

Front

What is the first step in completing the square for the equation n² - 2n - 3 = 0?

Back

Rearrange the equation to isolate the constant term: n² - 2n = 3.

Front

What do you do with the b value when completing the square?

Back

You divide it by 2 and then square the result.

Front

If you have the trinomial x² + 2x + c, what value of c makes it a perfect square?

Back

c = 1, because (2/2)² = 1.

Front

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

Back

Check if it can be factored into the form (x + a)², where a is a real number.

Front

What is the completed square form of the expression x² + 8x?

Back

The completed square form is (x + 4)² - 16.

Front

Solve the equation x² + 26x + c = 0 by completing the square. What is c?

Back

c = 169, because (26/2)² = 169.

Front

What is the significance of completing the square in solving quadratic equations?

Back

Completing the square allows you to rewrite a quadratic equation in vertex form, making it easier to solve and analyze.