Factoring and Quadratic Formula

Front

What is factoring in algebra?

Back

Factoring is the process of breaking down an expression into a product of simpler expressions, called factors.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does it mean for a quadratic equation to have 'zeroes'?

Back

Zeroes of a quadratic equation are the values of x that make the equation equal to zero.

Front

How do you factor the expression x² - 4?

Back

x² - 4 can be factored as (x - 2)(x + 2).

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.

Front

How can you determine if a quadratic can be factored easily?

Back

A quadratic can often be factored easily if the discriminant (b² - 4ac) is a perfect square.

Front

What is the discriminant in the quadratic formula?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, which determines the nature of the roots.

Front

What are the roots of the equation 2x² - 8x - 24 = 0?

Back

The roots are x = 6 and x = -2.

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in the form (x - p)(x - q) = 0, then set each factor to zero.

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.