Factoring Quadratics and Perfect Squares

The video tutorial explains how to rewrite a quadratic expression in the form a(x-h)^2 + k. It outlines four steps: checking the leading coefficient, forming a perfect square trinomial, undoing the added value, and factoring the trinomial. The tutorial concludes with the final expression form and its importance in graphing quadratic equations.

What is the main goal of rewriting the expression x^2 + 22x + 100?

• To simplify the expression

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

• To find the roots of the equation

• To convert it into a linear equation

What should you do if the leading coefficient is not one?

• Ignore the leading coefficient

• Multiply the expression by the leading coefficient

• Add a constant to the expression

• Factor out the leading coefficient

In step two, what is added to form a perfect square trinomial?

• The square of the constant term

• The square of the leading coefficient

• The product of the coefficients

• b divided by two squared

What is the value of b in the expression x^2 + 22x + 100?

• 100

• 22

• 11

• 1

Why do we subtract the same value added in step two?

• To maintain equality

• To factor the expression

• To simplify the expression

• To find the roots

What is the result of subtracting 121 from 100?

• 21

• 0

• -21

• 121

What does the trinomial factor into in step four?

• x + 11

• x - 11

• x - 11 squared

• x + 11 squared

What is the value of h in the expression a(x-h)^2 + k?

• -11

• -21

• 11

• 21

What is the value of k in the expression a(x-h)^2 + k?

• 11

• -11

• 21

• -21

Why is it important to express the quadratic in the form a(x-h)^2 + k?

• To find the derivative

• To solve linear equations

• To graph quadratic equations

• To simplify calculations