Solving Quadratic Equations - Factoring

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 are the methods to solve quadratic equations?

Back

The methods to solve quadratic equations include factoring, completing the square, using the quadratic formula, and graphing.

Front

What is factoring in the context of quadratic equations?

Back

Factoring is the process of expressing a quadratic equation as a product of its linear factors.

Front

How do you factor a quadratic equation of the form x² + bx + c?

Back

To factor a quadratic equation of the form x² + bx + c, find two numbers that multiply to c and add to b, then express it as (x + m)(x + n) where m and n are the two numbers.

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 apply the zero-product property to solve quadratic equations?

Back

To apply the zero-product property, set each factor of the factored quadratic equation equal to zero and solve for the variable.

Front

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

Back

The discriminant (D = b² - 4ac) determines the nature of the roots of a quadratic equation: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Front

What does it mean for a quadratic equation to have complex roots?

Back

A quadratic equation has complex roots when the discriminant is negative, resulting in roots that are not real numbers and can be expressed in the form a + bi.

Front

How can you solve a quadratic equation by completing the square?

Back

To solve by completing the square, rearrange the equation to isolate the constant term, then add the square of half the coefficient of x to both sides, and factor the left side.

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.