Completing the Square: Transforming Quadratic Equations

This video tutorial teaches how to transform quadratic equations by completing the square. It begins with an introduction to the concept using model pieces to represent different terms in the equation. The tutorial then demonstrates how to build a square model with given quadratic expressions, explaining the dimensions and calculations involved. It provides step-by-step guidance on completing the square for specific quadratic equations, such as X^2 + 6X and X^2 + 8X + 7, showing how to rearrange terms and add necessary values to form perfect squares. The lesson concludes with a transformation of the quadratic equation, emphasizing the equivalence of different forms.

What is the value of the long green bar in the model?

• X

• -1

• 1

• -X

What is the common misunderstanding when multiplying X by X?

• X * X is 4X

• X * X is X^2

• X * X is X

• X * X is 2X

How do you rearrange X^2 + 6X to complete the square?

• X + 2 by X + 2

• X + 3 by X + 3

• X + 4 by X + 4

• X + 5 by X + 5

What is the missing number needed to complete the square for X^2 + 6X?

• 12

• 6

• 4

• 9

What is the completed square form of X^2 + 8X + 7?

• (X + 3)^2

• (X + 5)^2

• (X + 6)^2

• (X + 4)^2

How many more ones are needed to complete the square for X^2 + 8X?

• 10

• 7

• 9

• 8

What is the equivalent expression for (X + 4)^2?

• X^2 + 8X + 8

• X^2 + 16X + 16

• X^2 + 4X + 16

• X^2 + 8X + 16