Completing the Square

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 a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as (x - a)² or (x + a)².

Front

Identify the perfect square trinomial: x² - 10x + 25

Back

(x - 5)²

Front

What is the formula for completing the square for the quadratic equation ax² + bx + c?

Back

The formula is x = -b/2a ± √((b/2a)² - c/a).

Front

How do you find the value to complete the square for x² + bx?

Back

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

Front

What does the plus or minus symbol (±) indicate in solving quadratics?

Back

It indicates that there are two possible solutions when taking the square root of both sides.

Front

Complete the square for the expression x² + 4x + ___.

Back

4 (the completed square is (x + 2)²).

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.

Front

Is x² + 6x + 9 a perfect square trinomial?

Back

Yes, it can be factored as (x + 3)².

Front

What is the first step in completing the square for x² + 8x?

Back

Take half of 8, which is 4, and square it to get 16.