Completing the Square Concepts

The video tutorial explains the process of completing the square, starting with factoring out the leading coefficient to make it one. It then guides through creating a perfect square trinomial by taking half of the b value, squaring it, and adjusting the equation accordingly. The tutorial further explains how to factor the trinomial into a binomial square and simplify the expression. Finally, it demonstrates how to find the vertex and axis of symmetry of the quadratic equation.

What is the first step in completing the square when 'a' is not equal to 1?

• Subtract a constant from both sides

• Factor out the coefficient of x²

• Multiply the equation by 2

• Add a constant to both sides

Why do we factor out the coefficient of x² in the process of completing the square?

• To find the vertex

• To simplify the equation

• To make 'a' equal to 1

• To eliminate x

What is the next step after factoring out the coefficient of x²?

• Divide the equation by 2

• Multiply the equation by 3

• Add a constant to both sides

• Create a perfect square trinomial

How do you create a perfect square trinomial?

• Multiply by a constant

• Add and subtract the same constant

• Divide by a constant

• Add a constant to one side only

What happens to the equation when you add and subtract the same constant?

• It becomes a perfect square trinomial

• It becomes a quadratic equation

• It becomes a linear equation

• It becomes a constant

What is the purpose of subtracting the constant outside the parentheses?

• To find the y-intercept

• To eliminate x

• To simplify the equation

• To balance the equation

What is the result of multiplying the added constant by the factored coefficient?

• A new variable

• A new coefficient

• A new equation

• A new constant

What is the purpose of creating a perfect square trinomial?

• To find the y-intercept

• To eliminate x

• To factor it into a binomial squared

• To simplify the equation

Why are perfect square trinomials useful?

• They can be easily solved

• They can be factored into binomials squared

• They eliminate the need for x

• They simplify the equation

What does a perfect square trinomial factor into?

• A quadratic equation

• A constant

• A linear equation

• A binomial squared