Lesson 4.6 - Quadratic Formula & Factoring

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does it mean for a quadratic equation to be factored?

Back

Factoring a quadratic equation means expressing it as a product of two binomials, such as (x + p)(x + q), where p and q are the roots of the equation.

Front

Solve the quadratic equation: -2x² + 4x = 9

Back

x = (-4 ± i√56)/-4.

Front

Factor the quadratic expression: 4x² - 16x - 9

Back

(2x - 9)(2x + 1).

Front

Factor the quadratic expression: x² + 12x + 35

Back

(x + 5)(x + 7).

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. It 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 roots.

Front

What does a zero discriminant indicate?

Back

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

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that the quadratic equation has two complex (non-real) roots.

Front

Solve the quadratic equation: -8k² - k + 2 = 0

Back

k = -0.57, 0.44.