Completing the Square Techniques

This video tutorial teaches how to rewrite quadratic expressions by completing the square. It explains the concept of vertex form and demonstrates the process using both visual area blocks and algebraic methods. The tutorial includes examples such as x^2 + 8x + 2, x^2 - 14x + 1, and x^2 + 5x + 2, showing step-by-step how to transform these expressions into perfect square trinomials and maintain equivalence with the original expressions.

What is the vertex form of a quadratic expression?

• An expression with no variable terms.

• An expression where all terms are constants.

• An expression where the variable term is linear.

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

In the area block method, what do you do after dividing the long blocks into two equal groups?

• Add them to the constant term.

• Arrange them around the square block.

• Remove them from the expression.

• Multiply them by the square block.

When completing the square for x^2 + 8x + 2, what is added to the variable terms to form a perfect square trinomial?

• 16

• 8

• 2

• 4

Why do we subtract the same number of units added to the variable terms when completing the square?

• To make the expression more complex.

• To simplify the expression.

• To maintain equivalence with the original expression.

• To eliminate the constant term.

What is the first step in completing the square for x^2 - 14x + 1?

• Subtract 1 from the expression.

• Group the variable terms using parentheses.

• Add 14 to the expression.

• Multiply the expression by 2.

What is the result of squaring half of the linear coefficient in x^2 - 14x + 1?

• 28

• 7

• 49

• 14

In the expression x^2 + 5x + 2, what is the value of 5/2 squared?

• 5

• 25/4

• 10/4

• 5/4

What is the vertex form of x^2 + 5x + 2 after completing the square?

• x + 5/2 squared minus 17/4

• x + 5 squared minus 2

• x + 2 squared minus 5

• x + 5/2 squared plus 17/4

What is the purpose of completing the square in a quadratic expression?

• To convert it into a linear expression.

• To rewrite it in vertex form.

• To eliminate the constant term.

• To find the roots of the expression.

What is the final step in completing the square for any quadratic expression?

• Add the constant term to the variable terms.

• Rewrite the perfect square trinomial in factored form.

• Multiply the expression by a constant.

• Divide the expression by the linear coefficient.