Identifying the transformations of a quadratic by completing the square

The video tutorial explains the process of completing the square for quadratic equations. It begins by rewriting the equation in descending order and factoring out a negative one if necessary. The instructor then demonstrates how to create a perfect square trinomial by dividing the B term by two and squaring it. Adjustments are made to the equation to maintain balance, and the trinomial is factored into a binomial squared. Finally, the video covers graphing the function, identifying the vertex, and understanding transformations such as shifts and reflections.

Why is it necessary to factor out a negative one when completing the square if 'a' is not equal to 1?

• To simplify the equation

• To ensure 'a' equals 1 for completing the square

• To make the equation more complex

• To change the sign of 'b'

What is the result of dividing 'B' by 2 and squaring it in the process of completing the square?

• A binomial

• A perfect square trinomial

• A quadratic equation

• A linear equation

When adding the squared value inside the parentheses, why must it also be subtracted?

• To maintain the balance of the equation

• To make the equation more complex

• To simplify the equation

• To change the sign of 'b'

What transformation occurs to the graph when the vertex is at (-8, 74) and there is a negative sign outside?

• Shift left 8 units, up 74 units, and reflect over the X-axis

• Shift left 8 units, down 74 units, and reflect over the Y-axis

• Shift right 8 units, down 74 units, and reflect over the Y-axis

• Shift right 8 units, up 74 units, and reflect over the X-axis

What is the final form of the equation after completing the square?

• A cubic equation

• A linear equation

• A binomial squared

• A quadratic equation