Understanding Square Area and Quadratic Equations

The video tutorial explains how to solve a problem involving a square whose sides are increased by 3 inches, resulting in an area nine times larger. The process involves modeling the problem, forming a quadratic equation, factoring it, and solving for the original side length. The solution reveals that the original side length is 3 inches.

What happens to the area of a square when each side is increased by 3 inches?

• The area is doubled.

• The area is tripled.

• The area is multiplied by 9.

• The area remains the same.

If the original side of a square is x, what is the side length of the enlarged square?

• x + 1

• x + 3

• x + 2

• x + 4

What is the area of the original square if its side is x?

• 3x

• x^2

• x

• 2x

How do you express the area of the enlarged square?

• x^2 + 9

• x^2 + 6x + 9

• x^2 + 3

• (x + 3)^2

What equation is formed when the area of the enlarged square is set to 9 times the area of the original square?

• 9(x + 3) = x^2

• x^2 = 9x

• x^2 = 9(x + 3)^2

• 9x^2 = (x + 3)^2

What is the first step in solving the quadratic equation 9x^2 = x^2 + 6x + 9?

• Multiply both sides by 9.

• Subtract 9x^2 from both sides.

• Subtract x^2 from both sides.

• Add 9x^2 to both sides.

What are the factors of the trinomial 8x^2 - 6x - 9?

• (4x - 3)(2x - 3)

• (4x - 3)(2x + 3)

• (4x + 3)(2x - 3)

• (4x + 3)(2x + 3)

What is the solution for x when solving 4x + 3 = 0?

• x = 3

• x = -3/4

• x = 3/4

• x = -3

What is the solution for x when solving 2x - 3 = 0?

• x = 3/2

• x = -3/2

• x = 2/3

• x = -2/3

What is the side length of the original square?

• 3 inches

• 1.5 inches

• 4 inches

• 2 inches