Transforming Quadratic Expressions

The video tutorial explains how to convert a quadratic expression from the form ax^2 + bx + c to a(x-h)^2 + k. It outlines four steps: factoring the coefficient of x^2, forming a perfect square trinomial, undoing the added value, and factoring the trinomial. The example used is 9x^2 - 36x - 3, which is converted to 9(x-2)^2 - 39. The tutorial emphasizes understanding each step to achieve the desired expression form.

What is the goal of transforming a quadratic expression into vertex form?

• To find the roots of the equation

• To simplify the expression

• To express it as a product of linear factors

• To rewrite it in the form a(x-h)^2 + k

In the expression 9x^2 - 36x - 3, what is the value of 'a' that needs to be factored out?

• 1

• 9

• 36

• 3

What constant should be added to form a perfect square trinomial from x^2 - 4x?

• 8

• 4

• 2

• 16

Why do we need to subtract 36 after adding 4 in the process of completing the square?

• To balance the equation

• To simplify the expression

• To find the roots

• To factor the trinomial

What is the final form of the expression after completing all steps?

• 9(x-2)^2 + 39

• 9(x+2)^2 - 39

• 9(x-2)^2 - 39

• 9(x+2)^2 + 39

What is the value of 'h' in the vertex form of the expression?

• 2

• -4

• -2

• 4

What is the value of 'k' in the vertex form of the expression?

• 0

• -39

• 9

• 39

What is the purpose of factoring the trinomial in the final step?

• To find the roots

• To simplify the expression

• To express it in vertex form

• To eliminate the constant term

Which of the following is a characteristic of a perfect square trinomial?

• It can be factored into a binomial squared

• It is always positive

• It has no real roots

• It has two distinct roots

What is the significance of the coefficient 'a' in the vertex form of a quadratic expression?

• It shifts the parabola horizontally

• It affects the width of the parabola

• It determines the direction of the parabola

• It shifts the parabola vertically