Quadratic Equations: Completing the Square

This video tutorial explains how to solve quadratic equations by completing the square. It begins with a basic introduction to the method, followed by detailed step-by-step solutions to three example problems. The first example demonstrates the process with a simple quadratic equation, while the second example involves verifying the solutions. The third example introduces a more complex scenario with a leading coefficient, illustrating how to handle such cases. The video also provides opportunities for practice and suggests additional resources for further learning.

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

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

• Take the square root of both sides.

• Multiply both sides by the leading coefficient.

• Factor the equation.

Tags

CCSS.HSA-REI.B.4B

When completing the square, what do you do with the middle coefficient?

• Multiply it by two.

• Divide it by two and then square it.

• Add it to the constant term.

• Subtract it from the constant term.

Tags

CCSS.HSA-REI.B.4B

How do you verify the solutions of a quadratic equation?

• By checking the discriminant.

• By substituting the solutions back into the original equation.

• By graphing the equation.

• By factoring the equation again.

Tags

CCSS.HSA-REI.B.4B

What is the purpose of taking the square root of both sides in the solving process?

• To eliminate the constant term.

• To simplify the equation.

• To isolate the variable.

• To factor the equation.

Tags

CCSS.HSA-REI.B.4B

In the practice example, what is the first step after moving the constant term?

• Factor the trinomial.

• Complete the square.

• Add the constant term back.

• Take the square root of both sides.

Tags

CCSS.7.NS.A.1C

What is the result of adding negative 12 and 49/4 in the practice example?

• Negative 1/4

• 1/4

• Negative 12

• Positive 12

Tags

CCSS.HSA-REI.B.4B

In the practice example, what is the final step to find the solutions?

• Move the term with the variable to the other side.

• Subtract the middle coefficient from both sides.

• Add the constant term back to the equation.

• Take the square root of both sides.

Tags

CCSS.HSA-REI.B.4B

In the advanced example, what must be done before completing the square?

• Divide the entire equation by the leading coefficient.

• Subtract the leading coefficient from both sides.

• Factor out the leading coefficient.

• Add the leading coefficient to both sides.

Tags

CCSS.HSA-REI.B.4B

How do you handle a leading coefficient that is not one in a quadratic equation?

• Ignore it and proceed with completing the square.

• Factor it out before completing the square.

• Add it to the constant term.

• Multiply it by the middle coefficient.

Tags

CCSS.6.NS.A.1

What is the result of dividing 7/2 by 2 in the advanced example?

• 3.5

• 14/2

• 7/8

• 7/4

Tags

CCSS.6.NS.A.1