GCSE Secondary Maths Age 13-17 - Algebra: Completing the Square - Explained

The video tutorial explains how to rewrite a quadratic equation in the form of (x + b)^2 + c by completing the square. It begins with factorizing the quadratic expression and then demonstrates the steps to complete the square. The tutorial also covers how to find the turning point of the quadratic graph using the completed square form. The process is broken down into clear steps, emphasizing key points such as factorization and the significance of the coefficient of x. The video concludes with a review of the method and its application in solving quadratic equations.

What is the first step in rewriting the quadratic expression 2x^2 + 16x + 35 in the form (x + b)^2 + c?

• Add 35 to both sides

• Factor out the coefficient of x^2

• Multiply the entire expression by 2

• Subtract 16 from both sides

Why is it important to factor out the coefficient of x^2 when completing the square?

• To make the expression a perfect square

• To eliminate the constant term

• To ensure the coefficient of x^2 is 1

• To simplify the expression

What is the significance of taking half the coefficient of x in the process of completing the square?

• It simplifies the quadratic expression

• It determines the value to be squared and added inside the bracket

• It eliminates the x term

• It helps in finding the constant term

How do you determine the x-coordinate of the turning point from the completed square form?

• It is the same as the coefficient of x

• It is twice the coefficient of x

• It is the opposite sign of the value inside the bracket

• It is the constant term

What is the y-coordinate of the turning point in the completed square form?

• The constant term outside the bracket

• The coefficient of x

• The value inside the bracket

• The product of the coefficients