Solving Quadratic Equations by Factoring

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 equation?

Back

Factoring a quadratic equation involves rewriting it as a product of two binomials, such as (x + p)(x + q) = 0, where p and q are the roots of the equation.

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 solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, first factor the equation into two binomials, then set each binomial equal to zero and solve for the variable.

Front

What are the steps to factor a quadratic equation?

Back

1. Write the equation in standard form (ax² + bx + c = 0). 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the middle term using these numbers. 4. Factor by grouping.

Front

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

Back

(x - 2)(x - 3) = 0.

Front

What are the solutions to the equation (x + 4)(x - 1) = 0?

Back

x = -4 and x = 1.

Front

How do you check if your factored solutions are correct?

Back

Substitute the solutions back into the original equation to see if they satisfy the 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, two complex roots.

Front

What is the vertex form of a quadratic equation?

Back

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