Completing 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 standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

How do you complete the square for the expression x² + 6x?

Back

Add (6/2)² = 9 to both sides to get (x + 3)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.

Front

What is the first step in completing the square?

Back

Move the constant term to the other side of the equation.

Front

How do you find the roots of a quadratic equation after completing the square?

Back

Set the equation to zero and solve for x by taking the square root of both sides.

Front

What does the term 'discriminant' refer to in a quadratic equation?

Back

The discriminant is b² - 4ac and determines the nature of the roots.

Front

If the discriminant is positive, what can be said about the roots?

Back

There are two distinct real roots.

Front

If the discriminant is zero, what can be said about the roots?

Back

There is exactly one real root (a repeated root).

Front

If the discriminant is negative, what can be said about the roots?

Back

There are no real roots; the roots are complex.