Deriving the Quadratic Formula by Completing the Square

This video tutorial teaches how to derive the quadratic formula by completing the square. It begins with an introduction to quadratic expressions and their components, followed by a detailed explanation of factoring perfect square trinomials. The main focus is on the step-by-step derivation of the quadratic formula, highlighting key steps such as setting the equation to zero, dividing by 'a', and manipulating terms to complete the square. The tutorial concludes with the final quadratic formula, emphasizing the importance of understanding each step in the process.

What are the values of a, b, and c in the expression 2x² + 5x + 8?

• a = 1, b = 5, c = 8

• a = 1, b = 6, c = 9

• a = 2, b = 5, c = 8

• a = 2, b = 6, c = 9

What is the first step in factoring a perfect square trinomial like x² + 12x + 36?

• Take half of the b term and square it

• Square the b term

• Subtract the c term

• Multiply the b term by 2

In the process of deriving the quadratic formula, what is done after setting the equation to zero?

• Subtract b from both sides

• Add c to both sides

• Divide by a on both sides

• Multiply by a on both sides

How do you find the new c term when completing the square in the quadratic formula derivation?

• Add the b term to a

• Multiply the b term by 2

• Divide the b term by 2 and square it

• Square the b term

What is the result of combining the fractions in the quadratic formula derivation?

• b² + 4ac over 2a

• b² - 4ac over 4a²

• b² + 4ac over 4a²

• b² - 4ac over 2a

What operation is performed to isolate x in the final steps of deriving the quadratic formula?

• Multiply by 2a

• Subtract b over 2a

• Add b over 2a

• Divide by 2a

What is the final form of the quadratic formula derived by completing the square?

• x = b ± √(b² - 4ac) / 2a

• x = -b ± √(b² - 4ac) / 2a

• x = b ± √(b² + 4ac) / 2a

• x = -b ± √(b² + 4ac) / 2a