How To Prove The Quadratic Formula By Completing The Square | Summary and Q&A

TL;DR

This video explains how to derive the quadratic formula by completing the square in the quadratic equation.

Key Insights

• ❎ The process of deriving the quadratic formula involves completing the square in the quadratic equation.
• 💯 Factoring a perfect square trinomial enables the transformation of the equation into a more manageable form.
• 🥺 Simplifying fractions and manipulating the equation lead to the final quadratic formula.

Transcript

in this video we're going to talk about how to derive the quadratic formula starting from this equation ax squared plus bx plus c is equal to zero the quadratic equation so how can we derive this particular formula x is equal to negative b plus or minus the square root of b squared minus 4ac all divided by 2a in order to derive that formula what we... Read More

Questions & Answers

Q: How can the quadratic formula be derived?

The quadratic formula can be derived by completing the square in the quadratic equation, which involves manipulation and simplification of the equation step-by-step. This process reveals the root values of x.

Q: What is the purpose of completing the square in the derivation process?

Completing the square allows us to transform the quadratic equation into a perfect square trinomial, making it easier to factor and find the roots. It simplifies the equation and leads to the quadratic formula.

Q: Why is it necessary to simplify fractions in the derivation?

Simplifying fractions is necessary to combine the expressions on the right side of the equation into a single fraction. This allows for a more concise representation of the quadratic formula, avoiding unnecessary complexity.

Q: What are the values represented by the ± symbol in the quadratic formula?

The ± symbol indicates that there are two possible solutions for x, which correspond to the two roots of the quadratic equation. The plus and minus signs determine the positive and negative versions of the solutions.

Summary & Key Takeaways

• The video demonstrates the step-by-step process of deriving the quadratic formula starting from the equation ax^2 + bx + c = 0.

• By completing the square, the equation is transformed into a perfect square trinomial, allowing for factorization.

• After rearranging the equation and simplifying fractions, the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a) is obtained.