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

What does 'a' represent in the quadratic equation ax² + bx + c = 0?

Back

'a' is the coefficient of x² and determines the direction of the parabola (upward if a > 0, downward if a < 0).

Front

What does 'b' represent in the quadratic equation ax² + bx + c = 0?

Back

'b' is the coefficient of x and affects the position of the vertex of the parabola.

Front

What does 'c' represent in the quadratic equation ax² + bx + c = 0?

Back

'c' is the constant term and represents the y-intercept of the parabola.

Front

What is the discriminant in the quadratic formula?

Back

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

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that there are two distinct real solutions to the quadratic equation.

Front

What does a zero discriminant indicate?

Back

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

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that there are no real solutions, only complex solutions.

Front

Solve using the quadratic formula: 2x² - 9x - 35 = 0

Back

x = -5/2, x = 7.

Front

Solve using the quadratic formula: 4x² + 4x + 1 = 0

Back

x = -½.