Factoring Quadratics

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is 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 means rewriting it as a product of two binomials.

Front

What is the factored form of x² + 5x + 6?

Back

(x + 2)(x + 3)

Front

How do you determine the factors of a quadratic expression?

Back

To determine the factors, find two numbers that multiply to 'c' (the constant term) and add to 'b' (the coefficient of x).

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

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; if negative, no real roots.

Front

What is the factored form of y² - 9?

Back

(y - 3)(y + 3) (This is a difference of squares.)

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic in the form (x - p)² = q to make it easier to solve or factor.

Front

What is the factored form of x² - 4x - 12?

Back

(x - 6)(x + 2) (Factors are -6 and +2.)

Front

What is the relationship between the roots and the factors of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that make the equation equal to zero, and they correspond to the values that make each factor equal to zero.