Factoring and Transforming Quadratic Expressions

The video tutorial explains how to rewrite a quadratic expression in the form a(x-h)^2 + k. It outlines four steps: factoring the coefficient of the quadratic term, forming a perfect square trinomial, undoing the added value, and factoring the trinomial. The tutorial provides a detailed walkthrough of each step, ensuring a clear understanding of the process.

What is the first step in transforming the quadratic expression -2x^2 + 12x - 9?

• Multiply the expression by 2

• Divide the expression by x

• Add a constant to the expression

• Factor out the coefficient of x^2

What is the value of 'a' in the expression -2x^2 + 12x - 9?

• 12

• -2

• 1

• -9

How do you form a perfect square trinomial from the expression -2(x^2 - 6x)?

• Multiply by 3 inside the parentheses

• Subtract 9 inside the parentheses

• Divide by 2 inside the parentheses

• Add 9 inside the parentheses

What is the coefficient of x inside the parentheses after factoring?

• -3

• 3

• 6

• -6

What is the purpose of adding a constant to form a perfect square trinomial?

• To complete the square

• To factor the expression

• To simplify the expression

• To balance the equation

What must be done to undo the effect of adding a constant inside the parentheses?

• Divide the constant by 2 and add it outside

• Multiply the constant by -2 and add it outside

• Subtract the same constant outside the parentheses

• Add the same constant outside the parentheses

What is the result of distributing -2 over the added constant 9?

• 9

• -9

• 18

• -18

What is the final form of the expression after factoring the perfect square trinomial?

• 2(x - 3)^2 + 9

• -2(x + 3)^2 - 9

• -2(x - 3)^2 + 9

• 2(x + 3)^2 - 9

What is the value of 'h' in the final expression -2(x - 3)^2 + 9?

• 3

• -3

• 9

• -9

What is the value of 'k' in the final expression -2(x - 3)^2 + 9?

• -9

• 9

• -3

• 3