2023 - 2024 - Solving Quadratics by Factoring and Square Roots

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 and a ≠ 0.

Front

What does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression means rewriting it as a product of two binomials, such as (px + q)(rx + s).

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 solve a quadratic equation by factoring?

Back

To solve a quadratic equation by factoring, set the equation to zero, factor the quadratic, and then use the Zero Product Property to find the solutions.

Front

What is the square root of a number?

Back

The square root of a number x is a value y such that y² = x.

Front

What is the relationship between the roots of a quadratic equation and its graph?

Back

The roots of a quadratic equation are the x-intercepts of its graph, where the graph intersects the x-axis.

Front

How do you find the roots of the equation x² = 16?

Back

To find the roots, take the square root of both sides: x = ±4.

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. It determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).