Mastering Quadratic Equations through Completing the Square

Why is the method of completing the square particularly useful?

• It is useful for quadratic equations that are not factorable.

• It only works for linear equations.

• It is the fastest method for solving any equation.

• It works for all types of equations.

What is the result of squaring the binomial (x + 4)?

• x^2 + 4

• x^2 + 16

• x^2 + 4x + 4

• x^2 + 8x + 16

What is the relationship between the linear term and the constant in a perfect square trinomial?

• The linear term is half the constant.

• The linear term is the square of the constant.

• The linear term is double the constant.

• The linear term is twice the square root of the constant.

How do you determine the number to add to a binomial to make it a perfect square trinomial?

• Square the linear coefficient.

• Divide the linear coefficient by 2 and then square it.

• Double the linear coefficient.

• Subtract the linear coefficient from the constant.

What is the first step in solving a quadratic equation by completing the square?

• Add a constant to both sides.

• Divide the linear coefficient by 2.

• Move the constant term to the other side of the equation.

• Multiply both sides by 2.

After moving the constant term to the other side, what is the next step in completing the square?

• Subtract the linear coefficient from the constant.

• Divide the linear coefficient by 2 and square it.

• Add the same constant to both sides.

• Multiply the linear coefficient by 2.

What do you do after creating a perfect square trinomial in the equation?

• Multiply both sides by 2.

• Add the same constant to both sides.

• Factor the trinomial.

• Take the square root of both sides.

What must be considered when taking the square root of both sides of an equation?

• Neither root.

• Both the positive and negative roots.

• Only the negative root.

• Only the positive root.

What is the final step in solving a quadratic equation by completing the square?

• Subtract the linear coefficient from both sides.

• Multiply both sides by 2.

• Add the same constant to both sides.

• Isolate the variable by adding or subtracting the constant.

How do you simplify the final solution if the square root is an irrational number?

• Multiply it by 2.

• Ignore the square root.

• Approximate it to the nearest whole number.

• Leave it in the square root form.