Completing the Square and Quadratics

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 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

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 is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

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

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real solution (a repeated root).

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has two complex (imaginary) solutions.

Front

How do you isolate x² in the equation x² - 6x - 27 = 0?

Back

To isolate x², you can add 27 to both sides, resulting in x² - 6x = 27.

Front

What is the first step in completing the square for the equation a² + 10a + 21 = 0?

Back

The first step is to subtract 21 from both sides, resulting in a² + 10a = -21.

Front

In the equation x² = 9 - 4x, what should be moved to complete the square?

Back

The term -4x should be moved to the left side to isolate x².