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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

There are two distinct real roots.

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

There are no real roots; the roots are complex.

Tags

CCSS.HSA-REI.B.4B