This video tutorial covers the process of completing the square, especially when dealing with fractions or when the coefficient 'a' is not equal to 1. The instructor provides three examples, demonstrating how to transform quadratic equations into vertex form. The first example focuses on factoring out a coefficient, the second deals with fractions, and the third combines both techniques. The video aims to simplify the process and help students understand the steps involved in completing the square.

What is the first step when completing the square if the coefficient of x^2 is not 1?

• Add the coefficient to both sides

• Factor out the coefficient from the first two terms

• Divide the entire equation by the coefficient

• Ignore the coefficient

In the first example, what value is added and subtracted inside the parentheses?

• 9

• 6

• 3

• 18

Why do fractions appear in the second example of completing the square?

• The coefficient of x^2 is a fraction

• The equation is already in vertex form

• The middle term is not divisible by 2

• The constant term is a fraction

What is the common denominator used to combine terms in the second example?

• 16

• 8

• 2

• 4

In the third example, what is the simplified form of 9/16 when multiplied by 2?

• 1/16

• 1/8

• 9/8

• 18/16

What is the vertex form of the equation in the third example?

• y = 2(x + 3/4)^2 + 1/8

• y = 2(x - 3/4)^2 + 1/8

• y = 2(x + 3/4)^2 - 1/8

• y = 2(x - 3/4)^2 - 1/8

What is the vertex of the equation in the third example?

• (-3/4, 1/8)

• (3/4, 1/8)

• (-3/4, -1/8)

• (3/4, -1/8)