Solving Quadratic Equations (All Methods + Complex Solutions)

Front

What does it mean if b² - 4ac = 0 in a quadratic equation?

Back

The quadratic equation has a real double solution.

Front

What does it mean if b² - 4ac > 0 in a quadratic equation?

Back

The quadratic equation has two real solutions that are different.

Front

What does it mean if b² - 4ac < 0 in a quadratic equation?

Back

The quadratic equation has two imaginary solutions that are different.

Front

Solve for x: x² + 2x - 24 = 0

Back

x = -6, x = 4

Front

Solve for x: x² - 4x + 4 = 0

Back

x = 2 (real double solution).

Front

What is the quadratic formula?

Back

x = (-b ± √(b² - 4ac)) / (2a) for solving quadratic equations.

Front

What are the types of solutions for quadratic equations?

Back

1. Two distinct real solutions 2. One real double solution 3. Two distinct imaginary solutions.

Front

What is the vertex form of a quadratic equation?

Back

y = a(x - h)² + k, where (h, k) is the vertex.

Front

How do you determine the number of solutions of a quadratic equation?

Back

By evaluating the discriminant (b² - 4ac).

Front

What is the axis of symmetry in a quadratic equation?

Back

The line x = -b/(2a) is the axis of symmetry.