Question

Discussion Topic

Solving quadratic equations is one of the main topics of this unit. Some quadratic equations can be solved with only one method, some can be solved with multiple methods, and some can’t be solved at all. Think about a task in your daily life that can be accomplished in a variety of ways. How do you decide the best course of action for accomplishing that task? How is this process like choosing a method for solving a quadratic equation that can be solved in multiple ways?

Answer 1

Answer:

  The Quadratic Formula: Given a quadratic equation in the following form:

ax2 + bx + c = 0

...where a, b, and c are the numerical coefficients of the terms of the quadratic, the value of the variable x is given by the following equation:

\small{ x = \dfrac{-b \pm \sqrt{b^2 - 4ac\phantom{\big|}}}{2a} }x=2a−b±b2−4ac∣∣∣

The nice thing about the Quadratic Formula is that the Quadratic Formula always works. There are some quadratics (most of them, actually) that we can't solve by factoring. But the Quadratic Formula will always spit out an answer, whether or not the quadratic expression was factorable.

Let's try that first problem from the previous page again, but this time we'll use the Quadratic Formula instead of the laborious process of completing the square:

Use the Quadratic Formula to solve x2 – 4x – 8 = 0

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