solving by completing the square by factoring out a two

The video tutorial explains the process of completing the square for a quadratic equation. It begins with factoring and adjusting the equation to eliminate any coefficient in front of the x² term. The instructor then demonstrates how to create a perfect square trinomial and find the vertex of the equation. Finally, the tutorial covers solving the equation to find its zeros, emphasizing the importance of correctly handling operations like division and square roots.

What is the first step in completing the square for the function f(x) = 2x^2 - x + 1?

• Multiply by 2

• Add 1 to both sides

• Subtract 1 from both sides

• Factor out the coefficient of x^2

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

• Divide it by 2 and square the result

• Add it to the constant term

• Subtract it from the constant term

• Multiply it by 2

How do you form a perfect square trinomial?

• By dividing the quadratic term by 2

• By subtracting the linear term from the constant

• By multiplying the linear term by 2

• By adding and subtracting the same constant

What is the vertex form of the function after completing the square?

• 2(x + 1/4)^2 + 7/8

• 2(x - 1/4)^2 + 7/8

• 2(x - 1/2)^2 + 1/8

• 2(x + 1/2)^2 + 1/8

What must be done before taking the square root when solving for zeros?

• Add 7/8 to both sides

• Multiply by 2

• Divide by 2

• Subtract 7/8 from both sides

What type of roots are obtained if the discriminant is negative?

• Integer roots

• Real roots

• Imaginary roots

• Rational roots

What is the final step in solving the equation after taking the square root?

• Add the linear term to both sides

• Subtract the constant term from both sides

• Add the constant term to both sides

• Subtract the linear term from both sides