Factoring a=1

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 the quadratic expression x² - 16x + 48?

Back

(x - 12)(x - 4)

Front

How do you find the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found by factoring, completing the square, or using the quadratic formula.

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 the quadratic expression n² - 13n + 40?

Back

(n - 5)(n - 8)

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 easily find its vertex and roots.

Front

What is the factored form of the quadratic expression k² + 7k + 10?

Back

(k + 2)(k + 5)

Front

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

Back

The sum of the roots is -b/a and the product of the roots is c/a, according to Vieta's formulas.