Solving 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 'complete the square'?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q, making it easier to solve for x.

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 factor a quadratic expression?

Back

To factor a quadratic expression ax² + bx + c, find two numbers that multiply to ac and add to b, then rewrite the expression as (x + m)(x + n), where m and n are the found numbers.

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. It determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

Solve by completing the square: v² + 6v - 59 = 0

Back

v = -3 ± 2√17.

Front

Factor the quadratic expression: x² + 7x + 12

Back

(x + 3)(x + 4).

Front

Solve by completing the square: x² - 10x - 11 = 0

Back

x = -1 and 11.

Front

Solve using the quadratic formula: a² - 4a + 4 = 0

Back

a = 2.

Front

Solve the quadratic equation: x² + 4x - 32 = 0

Back

x = -8, 4.