3.5 Solving Quadratics by Completing the Square

Front

What is the process of completing the square?

Back

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

Tags

CCSS.HSA-REI.B.4B

Front

What is the standard form of a quadratic equation?

Back

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

Front

How do you complete the square for the equation x² + 6x = 5?

Back

To complete the square, add (6/2)² = 9 to both sides: x² + 6x + 9 = 14, which simplifies to (x + 3)² = 14.

Tags

CCSS.HSA-REI.B.4B

Front

What is the value to add to complete the square for x² + 12x?

Back

To complete the square, add (12/2)² = 36, resulting in x² + 12x + 36.

Tags

CCSS.HSA-REI.B.4B

Front

What is the completed square form of x² + 6x?

Back

The completed square form is (x + 3)² - 9.

Tags

CCSS.HSA-REI.B.4B

Front

What is the value to add to complete the square for x² + 14x?

Back

To complete the square, add (14/2)² = 49, resulting in x² + 14x + 49.

Tags

CCSS.HSA-REI.B.4B

Front

How do you solve (2x - 1)² = 49?

Back

Take the square root of both sides: 2x - 1 = ±7. Solve for x to get x = 4 or x = -3.

Tags

CCSS.HSA-REI.B.4B

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

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

Back

The discriminant is the part of the quadratic formula under the square root: b² - 4ac. It determines the nature of the roots.

Tags

CCSS.HSA-REI.B.4B

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Tags

CCSS.HSA-REI.B.4B