Solving Quadratics by Factoring and Complete the Square

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of 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 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 zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you find the roots of a quadratic equation by factoring?

Back

To find the roots, set the factored equation to zero and solve for x.

Front

What is completing 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.

Front

What is the first step in completing the square for ax² + bx + c = 0?

Back

The first step is to move the constant term (c) to the other side of the equation.

Front

How do you complete the square for x² + 6x = 5?

Back

1. Move 5 to the left: x² + 6x - 5 = 0. 2. Take half of 6 (which is 3), square it (9), and add to both sides: (x + 3)² = 14.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What are the steps to solve x² + 4x - 32 = 0 by factoring?

Back

1. Factor the equation: (x + 8)(x - 4) = 0. 2. Set each factor to zero: x + 8 = 0 or x - 4 = 0. 3. Solve for x: x = -8 or x = 4.

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.