Completing the Square Techniques

The video tutorial explains how to complete the square, a method used when factoring is not possible or when converting a quadratic equation to vertex form. The process involves isolating variables, creating a perfect square trinomial by adding a calculated term to both sides, and then solving the equation. This method is useful for solving quadratic equations and graphing parabolas.

Why do we complete the square when solving quadratic equations?

• To convert a polynomial to its standard form

• To simplify linear equations

• To find the roots of linear equations

• To avoid using the quadratic formula

Which of the following is NOT a reason to complete the square?

• To convert to vertex form

• To solve quadratic equations

• To simplify linear equations

• To avoid the quadratic formula

What is the first step in completing the square?

• Multiply the equation by 2

• Isolate the constant term

• Isolate the variable terms

• Add a constant to both sides

How do you determine the third term to add when completing the square?

• Divide the middle term by 2 and square it

• Multiply the middle term by 2

• Add the middle term to the constant

• Subtract the middle term from the constant

What form does the trinomial take after completing the square?

• A cubic equation

• A linear equation

• A binomial squared

• A quadratic equation

What is the result of rewriting x^2 + 4x + 4 as a binomial squared?

• (x + 4)^2

• (x - 2)^2

• (x + 2)^2

• (x - 4)^2

What should you do after adding the third term to both sides of the equation?

• Subtract the third term from both sides

• Divide both sides by the third term

• Multiply both sides by 2

• Rewrite the left side as a binomial squared

How can completing the square help in graphing a parabola?

• It provides the x-intercepts directly

• It converts the equation to vertex form

• It eliminates the need for a graph

• It changes the parabola to a line

What is the vertex form of a quadratic equation useful for?

• Identifying the roots

• Calculating the slope

• Determining the axis of symmetry

• Finding the y-intercept

What is the next step after rewriting the trinomial as a binomial squared?

• Add another term to both sides

• Subtract the constant from both sides

• Solve for x by taking the square root

• Multiply the equation by 2