Completing the Square Check

Front

What is completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting them in the form (x + p)² = q, making it easier to find the roots.

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

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

Back

To make it a perfect square trinomial, c = (b/2)².

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression that can be factored into the square of a binomial, such as (x + a)² = x² + 2ax + a².

Front

Complete the square for x² + 12x + ____. What is the missing value?

Back

The missing value is 36.

Front

When factoring x² - 4x + 4 = 20, what goes in the blank? (x - __ )² = 20

Back

The blank is filled with 2.

Front

What is the first step to solving a² + 10a + 21 = 0 by completing the square?

Back

The first step is to subtract 21 from both sides.

Front

What value of c would make x² + 8x + c a perfect square trinomial?

Back

The value of c is 16.

Front

Complete the square for x² + 6x = 5. What is the resulting equation?

Back

The resulting equation is (x + 3)² = 14.

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 of the parabola.