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 the concept of completing the square and then moves on to preparing the quadratic equation for this process. The tutorial explains the detailed steps of completing the square using variables instead of numbers, ensuring the method works for any quadratic equation. Finally, it demonstrates how to derive the quadratic formula from the completed square, providing a comprehensive understanding of the process.

What is the first step in completing the square for a quadratic equation?

• Rearrange the terms

• Divide by the coefficient of x^2

• Add a constant to both sides

• Multiply by the coefficient of x

Why do we divide the entire quadratic equation by 'a'?

• To eliminate the constant term

• To make the coefficient of x^2 equal to 1

• To find the roots of the equation

• To simplify the equation

What do you add to both sides of the equation to complete the square?

• b^2/4a

• b^2/4a^2

• b/2a

• b^2/2a

What is the purpose of completing the square in a quadratic equation?

• To find the vertex of the parabola

• To convert it into a perfect square trinomial

• To factor the equation

• To eliminate the linear term

What is the result of taking the square root of both sides of the completed square equation?

• A constant value

• A binomial expression

• A quadratic equation

• A linear equation

What does the quadratic formula allow you to find?

• The roots of the quadratic equation

• The y-intercept

• The axis of symmetry

• The maximum value of the quadratic

What is the final form of the quadratic formula derived in this lesson?

• x = b ± sqrt(b^2 - 4ac) / 2a

• x = b ± sqrt(b^2 + 4ac) / 2a

• x = -b ± sqrt(b^2 - 4ac) / 2a

• x = -b ± sqrt(b^2 + 4ac) / 2a