Lesson 8: Discover | MoodleHUB 🎓

1. Lesson 8

1.4. Discover

Mathematics 20-2 M3 Lesson 8

Module 3: Quadratics

Discover

This image shows the quadratic formula x equals negative b plus or minus the square root of b squared minus 4ac all divided by 2a.

It is often easiest to factor when solving a quadratic equation, ax2 + bx + c = 0. You have used graphing technology to find the roots of equations that are not factorable. There is a third way to find the roots of a quadratic equation. You can use a formula called the quadratic formula. This formula always works, whether the original equation is factorable or not.

Did You Know?

The quadratic formula, , is a quick and efficient way to solve quadratic equations. The formula was discovered and has been used by many cultures going back well before 300 BCE.

Quadratic Formula Proof shows the derivation of the quadratic formula.

Watch Using the Quadratic Formula to see an example of using the quadratic formula to solve an equation that is not factorable.

Study “Example 2: Connecting the quadratic formula to factoring” on page 416 of the textbook. Pay attention to how the values for a, b, and c were substituted into the formula. Also, look closely at the note about the discriminant being a perfect square. This might be useful in some factoring questions.

Self-Check 1

Solve the equation 15x2 − 6 = x using the quadratic formula. Answer