Solving Quadratics

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 solve a quadratic equation?

Back

To solve a quadratic equation means to find the values of x that make the equation true, which are called the roots or solutions.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What is factoring in the context of quadratic equations?

Back

Factoring is the process of rewriting a quadratic equation as a product of two binomials, which can then be set to zero to find the solutions.

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?

Back

To apply the Zero Product Property, set each factor of the equation equal to zero and solve for the variable.

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 quadratic formula?

Back

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

Front

What does the discriminant tell you?

Back

The discriminant (b² - 4ac) indicates the nature of the roots of a quadratic equation: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

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

Back

To solve by completing the square, rearrange the equation, add a constant to both sides to form a perfect square trinomial, and then solve for x.