Quadratic Equations: Standard and Factored Forms

The video tutorial covers the process of converting quadratic equations into standard and factored forms. It begins with expanding a quadratic expression and simplifying it to achieve the standard form. The tutorial then demonstrates how to convert the standard form into factored form by identifying factors that multiply to a specific value and add up to another. The video also includes a section on expanding and simplifying expressions with additional terms and concludes with factoring using the greatest common factor. Throughout, the tutorial emphasizes understanding the steps and logic behind each transformation.

What is the first step in converting a quadratic equation into standard form?

• Expand the expression

• Find the greatest common factor

• Simplify the equation

• Identify the x-intercepts

When expanding (X + 3)^2, what is the result before simplification?

• X^2 + 9

• X^2 + 3X + 3

• X^2 + 6X + 9

• X^2 + 3X + 1

What are the factors of 8 that add up to 6?

• 2 and 4

• 4 and 2

• 1 and 8

• 3 and 5

How do you write the factored form of X^2 + 6X + 8?

• (X + 2)(X + 2)

• (X + 5)(X + 1)

• (X + 3)(X + 3)

• (X + 4)(X + 2)

What are the x-intercepts of the equation in factored form (X + 4)(X + 2)?

• 0 and -4

• -2 and 2

• -4 and -2

• 4 and 2

What is the result of expanding (X + 1)^2?

• X^2 + 2X + 1

• X^2 + 2X

• X^2 + 1

• X^2 + 1X + 1

What is the standard form of the equation after expanding and simplifying (X + 1)^2 + 32?

• X^2 + 2X + 30

• X^2 + 2X + 32

• X^2 + 2X + 33

• X^2 + 2X + 34

What is the greatest common factor in the equation -2X^2 - 4X + 30?

• 1

• -2

• 2

• -1

Which pair of numbers multiplies to -15 and adds up to 2?

• -5 and 3

• 5 and -3

• 3 and -5

• -3 and 5

What is the factored form of the equation -2(X^2 - 2X - 15)?

• -2(X - 5)(X + 3)

• -2(X + 5)(X - 3)

• -2(X - 3)(X + 5)

• -2(X + 3)(X - 5)