Quadratic Expression Transformation Quiz

The video tutorial explains how to convert a quadratic expression from the standard form ax^2 + bx + c to the vertex form a(x-h)^2 + k. It outlines four steps: factoring the coefficient if a is not 1, forming a perfect square trinomial, completing the square by adjusting constants, and finally factoring the trinomial to achieve the desired form. The tutorial provides a detailed walkthrough of each step, including factoring techniques and handling fractions, to help learners understand the process of completing the square.

What is the purpose of transforming a quadratic expression into the form a(x-h)^2 + k?

• To simplify the expression

• To find the roots of the equation

• To express it in vertex form

• To eliminate the constant term

In Step 1, if the coefficient of the x^2 term is not 1, what should you do?

• Factor it out from the x^2 and x terms

• Ignore it

• Add it to the constant term

• Multiply it by the entire expression

Why is it challenging to factor 3 from the expression 3x^2 + 4x?

• Because x is not a factor of 3

• Because 3 is not a factor of 4x

• Because 4x is a constant

• Because 3 is a prime number

What value is added inside the parentheses to form a perfect square trinomial in Step 2?

• b divided by 2 squared

• b times 2

• b squared

• b divided by 2

In Step 2, what is the simplified form of (2/3)^2?

• 2/9

• 2/3

• 4/3

• 4/9

What is the purpose of subtracting the added value in Step 3?

• To balance the equation

• To complete the square

• To simplify the expression

• To factor the trinomial

What is the common denominator used to find the difference in Step 4?

• 2

• 1

• 9

• 3

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

• 3(x + 2/3)^2 + 31/3

• 3(x - 2/3)^2 + 31/3

• 3(x + 2/3)^2 - 31/3

• 3(x - 2/3)^2 - 31/3

In the final expression, what is the value of h?

• -31/3

• 2/3

• -2/3

• 31/3

What is the value of k in the final expression?

• 31/3

• -2/3

• 2/3

• -31/3