Proving the Quadratic Formula Through Completing the Square

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?

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

• 8

• 2

• 4a

• 2a

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