Learn to complete the square to write a quadratic in vertex form

The video tutorial explains the process of factoring a quadratic equation to create a perfect square trinomial. It introduces step 1.5, which involves factoring out a number to make the leading coefficient one. The instructor demonstrates how to find the 'magic number' to complete the square and discusses the importance of maintaining balance by adding and subtracting the same value. The tutorial also covers the concepts of vertex and range in quadratic equations, emphasizing the impact of negative coefficients on graph orientation. The lesson concludes with a summary of the key points discussed.

What is the purpose of factoring out a negative two in the equation?

• To eliminate the variable

• To make the leading coefficient equal to one

• To simplify the equation

• To make the equation equal to zero

How do you determine the 'magic number' to complete the square?

• By multiplying the coefficient of x by 2

• By dividing the coefficient of x by 2 and squaring it

• By adding the coefficients of x and x^2

• By subtracting the constant term

Why is it necessary to subtract the magic number after adding it?

• To make the equation equal to zero

• To keep the equation balanced

• To simplify the equation

• To eliminate the variable

What must be considered when adding the magic number in terms of the distributive property?

• The magic number should be divided by the leading coefficient

• The magic number should be subtracted from the constant term

• The magic number should be multiplied by the factored out number

• The magic number should be added twice

What is the vertex of the quadratic function discussed in the video?

• (4, 33)

• (-4, -33)

• (4, -33)

• (-4, 33)

How does a negative sign outside the quadratic function affect its graph?

• It shifts the graph to the right

• It reflects the graph over the y-axis

• It reflects the graph over the x-axis

• It shifts the graph upwards

What is the range of the quadratic function discussed?

• Negative infinity to 33, not included

• Negative infinity to 33, included

• 0 to 33, included

• 0 to 33, not included