Quadratic Formula

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

Identify the values of a, b, and c in the equation: 4x² - 8x = 3.

Back

a = 4, b = -8, c = -3.

Front

What is the first step in solving the equation x² + 6x - 13 = 3?

Back

Subtract 3 from both sides to set the equation to zero.

Front

Solve using the Quadratic Formula: 4v² - 1v - 18 = 0.

Back

v = 2.25, -2.

Front

Solve using the Quadratic Formula: 2x² + x - 4 = 0.

Back

x = 1.19 and x = -1.69.

Front

What does 'b² - 4ac' represent in the Quadratic Formula?

Back

It is called the discriminant and determines the nature of the roots of the quadratic equation.

Front

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

Back

The quadratic equation has two distinct real roots.

Front

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

Back

The quadratic equation has exactly one real root (a repeated root).

Front

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

Back

The quadratic equation has two complex (non-real) roots.

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 and a ≠ 0.