Completing the Square Concepts

The video tutorial covers the process of completing the square, a method used to solve quadratic equations. It begins with an introduction to the concept and the importance of isolating the constant term. The tutorial explains the role of coefficients and the properties of a perfect square. It then guides viewers through finding the 'B' term and completing the square, followed by solving the equation using square roots. The lesson concludes with a verification of the solutions through graphing, ensuring the correctness of the method.

What is the first step in completing the square?

• Find the value of B

• Isolate the constant term

• Ensure the coefficient of x squared is 1

• Graph the equation

What should the coefficient of x squared be when completing the square?

• 2

• Any number

• 0

• 1

Which formula represents a perfect square trinomial?

• a^2 - 2ab + b^2

• a^2 - b^2

• a^2 + 2ab + b^2

• a^2 + b^2

How do you determine the value of B in the equation?

• By adding the constant term to both sides

• By dividing the middle term by 2

• By guessing

• By multiplying the constant term by 2

What must be done after adding a term to complete the square?

• Subtract the same term from both sides

• Add the same term to both sides

• Multiply both sides by the term

• Divide both sides by the term

What is the next step after factoring the completed square?

• Take the square root of both sides

• Add the constant term

• Subtract the constant term

• Multiply both sides by 2

What are the possible values of x after solving the equation?

• x = 2 and x = -2

• x = 4 and x = -5

• x = 5 and x = -4

• x = 0 and x = 1

How can you verify the solutions obtained from completing the square?

• By checking the discriminant

• By graphing the equation

• By solving another equation

• By using a calculator

What should the graph of the equation show if the solutions are correct?

• The graph should not intersect the x-axis

• The graph should be a straight line

• The graph should be a circle

• The graph should intersect the x-axis at the solutions

What are the roots of the equation x^2 - x - 20 = 0?

• x = 2 and x = -2

• x = 4 and x = -5

• x = 5 and x = -4

• x = 0 and x = 1