Complete the Square

Front

What is 'Completing the Square'?

Back

A method used to solve quadratic equations by rewriting them in the form (x + p)² = q.

Front

What is the first step in completing the square for the equation x² + 6x = 5?

Back

Subtract 5 from both sides to get x² + 6x - 5 = 0.

Front

How do you determine if a trinomial is a perfect square?

Back

A trinomial is a perfect square if it can be expressed as (x + a)² = x² + 2ax + a².

Front

What is the value of c that makes x² + 8x + c a perfect square trinomial?

Back

c = 16, because (8/2)² = 16.

Front

What is the value of c that makes x² - 12x + c a perfect square trinomial?

Back

c = 36, because (-12/2)² = 36.

Front

What is a perfect square trinomial?

Back

A trinomial that can be factored into the square of a binomial.

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

What does it mean to 'complete the square' in a quadratic equation?

Back

It means to transform the equation into a perfect square trinomial to facilitate solving.

Front

What is the result of completing the square for x² + 6x?

Back

(x + 3)² - 9.

Front

How do you find the vertex of a parabola from the completed square form?

Back

The vertex is at the point (-p, q) in the form (x + p)² = q.