Completing the Square in Quadratic Expressions

This video tutorial teaches how to complete the square in quadratic expressions using algebraic methods. It explains the concept of vertex form and demonstrates the process through area models and algebraic steps. The tutorial includes examples of completing the square for different quadratic expressions, emphasizing the creation of perfect square trinomials and maintaining equivalent expressions.

What is the vertex form of a quadratic expression?

• An expression where the variable term is a perfect square and the other term is a constant.

• An expression where all terms are constants.

• An expression where the variable term is linear.

• An expression where the variable term is cubic.

In the process of completing the square, what is the first step when using algebraic methods?

• Subtract the constant term.

• Divide the quadratic term by 2.

• Group the variable terms using parentheses.

• Multiply the linear term by 2.

When completing the square for the expression x^2 - 14x + 1, what value is added to the variable terms?

• 28

• 14

• 7

• 49

What is the result of completing the square for the expression x^2 + 5x + 2?

• x + 2 quantity squared minus 5

• x + 5/2 quantity squared minus 17/4

• x + 2.5 quantity squared minus 4.25

• x + 5 quantity squared minus 17

Why is it necessary to subtract the same number of units added to the variable terms when completing the square?

• To maintain an equivalent expression to the original.

• To eliminate the constant term.

• To simplify the expression.

• To make the expression a perfect square.