Solving Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What does it mean to factor a quadratic equation?

Back

Factoring a quadratic equation means expressing it as a product of two binomials, such as (x + p)(x + q) = 0.

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation.

Front

How do you find the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form y = ax² + bx + c can be found using the formula x = -b/(2a).

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 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 no real roots, but two complex roots.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form (x + p)(x + q) = 0, then set each factor to zero and solve for x.