Regents Exam: Algebra I August 2016 (Problem 21 of 37)

The video tutorial explains how to convert a quadratic function into its vertex form. It begins by introducing the quadratic function and the problem of finding an equivalent expression. Two methods are discussed: expanding and simplifying options or rewriting the function by completing the square. The process of completing the square involves grouping terms, factoring, and introducing constants to form a perfect square trinomial. The tutorial concludes by finalizing the vertex form and identifying the correct option that matches the original function.

What are the two methods mentioned for finding the equivalent vertex form of a quadratic function?

• Substituting values; Using a table

• Expanding and simplifying options; Completing the square

• Graphing the function; Using a calculator

• Guessing the answer; Asking a friend

What is the first step in the process of completing the square?

• Introducing a constant

• Grouping the quadratic and linear terms

• Factoring the entire expression

• Simplifying the constants

How do you determine the constant to introduce when completing the square?

• Divide the coefficient of the linear term by 2 and square it

• Multiply the linear term by 2

• Divide the coefficient of the quadratic term by 2 and square it

• Add the coefficients of the quadratic and linear terms

Why is it necessary to introduce the additive inverse when completing the square?

• To change the function's graph

• To make the expression more complex

• To simplify the expression

• To maintain balance or equality in the equation

What is the final vertex form of the quadratic function given in the tutorial?

• 3(x + 2)^2 + 1

• 3(x - 2)^2 - 1

• 3(x + 2)^2 - 1

• 3(x - 2)^2 + 1