Solving Quadratics by Completing the Square

The video tutorial covers the method of completing the square, starting with an introduction and overview. It provides a detailed step-by-step process for applying the method to a specific equation, including moving constants, completing the square, and solving the equation. The tutorial also includes an example problem and suggests practice problems for further learning. The video concludes with a summary and a preview of the next lesson, which will introduce a different method for solving equations with fractional answers.

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

• Take the square root of both sides.

• Divide all terms by the coefficient of x^2.

• Factor the quadratic equation.

• Move all constants to the right side of the equation.

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CCSS.HSA-REI.B.4B

What is the result of squaring -8 in the process of completing the square?

• -64

• -16

• 16

• 64

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CCSS.HSA-REI.B.4B

What value is added to both sides of the equation to complete the square?

• The square of half of the coefficient of x.

• The product of the coefficients of x^2 and x.

• Half of the constant term squared.

• The square root of the constant term.

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CCSS.HSA-REI.B.4B

What is the value of c when completing the square for the equation x^2 - 16x = -22?

• -64

• 8

• -8

• 64

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CCSS.HSA-REI.B.4B

What does the constant added to both sides of the equation represent in the process of completing the square?

• The product of the coefficients of x^2 and x.

• The square root of the constant term.

• The square of half of the coefficient of x.

• The square of the coefficient of x.

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CCSS.HSA-REI.B.4B

After completing the square, the equation is factored into what form?

• (x + a)^2

• (x - a)^2

• x^2 + (a+b)x + ab

• ax^2 + bx + c

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CCSS.HSA-REI.B.4B

What is the next step after factoring the completed square equation?

• Add the constant to both sides.

• Multiply both sides by the leading coefficient.

• Take the square root of both sides.

• Subtract the constant from both sides.

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CCSS.HSA-REI.B.4B

What do you do after taking the square root of both sides in the equation?

• Subtract the square root from both sides.

• Add the square root to both sides.

• Divide both sides by the coefficient of x.

• Move any constants to one side.

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What is the final form of the equation after completing the square and solving?

• x = 8 ± √86

• x = constant ± √86

• x = ±√constant

• x = -8 ± √86

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CCSS.HSA-REI.B.4B

Why do we not use completing the square for equations that result in fractional answers?

• It's too complicated.

• The results are not accurate.

• There's a more efficient method.

• It's not possible to complete the square for such equations.

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CCSS.HSA-REI.B.4B