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 ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the two characteristics to look for when solving a quadratic equation by factoring?

Back

A positive coefficient for x^2 and the equation set equal to 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 (px + q)(rx + s) = 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 apply the zero-product property to solve a quadratic equation?

Back

Set each factor equal to zero and solve for the variable.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0.

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 is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots of the quadratic equation: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

Front

What are the steps to factor a quadratic equation?

Back

1. Write the equation in standard form. 2. Identify a, b, and c. 3. Find two numbers that multiply to ac and add to b. 4. Rewrite the middle term using these numbers. 5. Factor by grouping.

Front

What is the role of the leading coefficient in a quadratic equation?

Back

The leading coefficient (a) affects the direction and width of the parabola: if a > 0, the parabola opens upwards; if a < 0, it opens downwards.