Solve Quadratics

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 does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression involves rewriting it as a product of its linear factors, if possible, such as (x - p)(x - q) where p and q are the roots.

Front

What is the quadratic formula?

Back

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

Front

How do you identify a, b, and c in a quadratic equation?

Back

In the standard form ax² + bx + c = 0, a is the coefficient of x², b is the coefficient of x, and c is the constant term.

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, also known as a repeated or double 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 factor the expression v² - 6v + 9?

Back

The expression factors to (v - 3)².

Front

What is the factored form of 81m² - 1?

Back

The expression factors to (9m - 1)(9m + 1).