Solving Quadratics 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, allowing for easier solutions to the equation.

Front

What are the steps to solve a quadratic equation by factoring?

Back

1. Write the equation in standard form (ax² + bx + c = 0). 2. Factor the quadratic expression. 3. Set each factor equal to zero. 4. Solve for the variable.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the values of x that satisfy the equation, often found by setting the equation equal to zero.

Front

How do you find the roots of the equation (x - 3)(x + 6) = 0?

Back

Set each factor equal to zero: x - 3 = 0 gives x = 3, and x + 6 = 0 gives x = -6. Thus, the roots are x = 3 and x = -6.

Front

What is the significance of the quadratic formula?

Back

The quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), provides a method to find the roots of any quadratic equation, even when factoring is difficult.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots (real and distinct, real and equal, or complex).

Front

How do you factor the quadratic x² + 7x + 12?

Back

To factor x² + 7x + 12, find two numbers that multiply to 12 and add to 7. The factors are (x + 3)(x + 4).

Front

What are the solutions to the equation x² - 9x + 20 = 0?

Back

Factoring gives (x - 4)(x - 5) = 0, leading to solutions x = 4 and x = 5.

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.