Proving the Quadratic Formula Through Completing the Square

This video tutorial explains how to derive the quadratic formula from the quadratic equation ax^2 + bx + c = 0. The process involves solving for x by completing the square, factoring the trinomial, and simplifying expressions. The tutorial guides through each step, including moving terms, dividing by coefficients, and combining fractions, ultimately leading to the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a.

What is the first step in deriving the quadratic formula from the quadratic equation?

• Take the square root of both sides

• Factor the equation

• Isolate the variable x

• Move the constant term to the other side

What operation is performed after moving the constant term to the other side in the equation?

• Subtraction of the linear coefficient

• Multiplication by the leading coefficient

• Division by the coefficient of x squared

• Addition of a new variable

What is the purpose of completing the square in the derivation of the quadratic formula?

• To eliminate the quadratic term

• To isolate the variable x

• To simplify the equation

• To create a perfect square trinomial

What term is added to both sides of the equation when completing the square?

• (a/2b)^2

• (b/2)^2

• (b/2a)^2

• (2a/b)^2

What is the result of squaring b/2a in the process?

• b^2/4a

• b^2/4a^2

• 4b^2/a

• 4a^2/b^2

How do you combine two fractions into one in the context of deriving the quadratic formula?

• By finding a common denominator

• By multiplying the numerators

• By adding the denominators

• By subtracting one fraction from the other

After combining the terms into a single fraction, what is the next step?

• Factor the trinomial

• Take the square root of both sides

• Multiply by the leading coefficient

• Divide by the common denominator

What is the final operation performed to isolate x in the quadratic formula derivation?

• Addition of the linear coefficient

• Subtraction of b over 2a from both sides

• Division by the coefficient of x

• Subtraction of the square root term

What does the square root of 4a^2 simplify to?

• 8

• 2

• 4a

• 2a

Which term is moved from the left side to the right side to help isolate x?

• b/2a

• b^2/4a^2

• 4ac/4a^2

• c/a