Completing the Square Techniques

The video tutorial explains how to convert quadratic functions from general form to vertex form using the completing the square technique. It covers the process step-by-step, including examples with negative and fractional coefficients, and highlights common mistakes to avoid. The tutorial emphasizes the importance of understanding the vertex form for graphing and analyzing quadratic functions.

What is the vertex form of a quadratic function?

• y = a(x + p)^2 - q

• y = ax + b

• y = a(x - p)^2 + q

• y = ax^2 + bx + c

Why is it useful to convert a quadratic function to vertex form?

• To simplify the equation

• To easily identify the vertex

• To eliminate the constant term

• To make the function linear

What technique is used to convert a quadratic function from general form to vertex form?

• Graphing

• Completing the square

• Factoring

• Using the quadratic formula

When completing the square, what should you do with the leading coefficient?

• Ignore it

• Factor it out of the first two terms

• Add it to the constant term

• Multiply it by the entire equation

In the process of completing the square, what do you add and subtract?

• The square of the constant term

• The square of half the coefficient of x

• The square of the leading coefficient

• The square of the entire equation

What is the vertex of the quadratic function y = 3(x - 3)^2 - 13?

• (-3, -13)

• (3, -13)

• (-3, 13)

• (3, 13)

How does the leading coefficient affect the direction of the parabola?

• A negative coefficient makes it open upwards

• A positive coefficient makes it open downwards

• A positive coefficient makes it open upwards

• It has no effect on the direction

What happens to the y-coordinate when you move one unit from the vertex in a quadratic function with a leading coefficient of 3?

• It decreases by 3

• It remains the same

• It doubles

• It increases by 3

In the example y = -5x^2 - 15x - 6, what is the first step in completing the square?

• Add 15 to both sides

• Add 6 to both sides

• Multiply the entire equation by -1

• Factor out -5 from the first two terms

When dealing with fractions in completing the square, what is recommended?

• Convert fractions to whole numbers

• Ignore the fractions

• Use fractions

• Use decimals