Solving Quadratic Equations

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 is the Quadratic Formula?

Back

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

Front

What does it mean to make an equation equal to zero?

Back

Making an equation equal to zero is a crucial step in solving quadratic equations, allowing us to apply factoring or the Quadratic Formula.

Front

How do you solve x² + 6x - 13 = 3?

Back

First, subtract 3 from both sides to get x² + 6x - 16 = 0.

Front

What is the first step in using the Quadratic Formula?

Back

Identify the coefficients a, b, and c from the quadratic equation in the form ax² + bx + c = 0.

Front

How do you solve 2x² + 6x = 7 using the Quadratic Formula?

Back

Rearrange to 2x² + 6x - 7 = 0, then apply the Quadratic Formula.

Front

What is the solution to -5x² = -50?

Back

x = ± √10.

Front

How do you solve x² = 16?

Back

Take the square root of both sides to get x = ± 4.

Front

What is the significance of the discriminant in the Quadratic Formula?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, two real solutions; if zero, one real solution; if negative, no real solutions.

Front

What are the steps to factor a quadratic equation?

Back

1. Write in standard form ax² + bx + c = 0. 2. Find two numbers that multiply to ac and add to b. 3. Rewrite the equation and factor.