Exploring the Difference of Squares

This lesson covers quadratic equations, focusing on factoring techniques such as the difference of squares and perfect square trinomials. It includes practice problems and demonstrates solving quadratics using square roots. The lesson emphasizes understanding the structure of quadratic equations and applying various methods to find solutions, including graphing and identifying intercepts and vertices.

What is the first step in factoring the quadratic equation y = 4x^2 - 16?

• Add a B term

• Divide by 4

• Rewrite as a trinomial

• Find the vertex

When factoring x^2 + 0x - 9, what are the factors?

• x - 1 and x + 9

• x - 3 and x + 3

• x - 4 and x + 4

• x - 9 and x + 1

What is the rule for factoring a quadratic in the form of a^2 - b^2?

• Quotient of squares

• Difference of squares

• Sum of squares

• Product of squares

What is the vertex form of the quadratic equation y = x^2 + 6x + 9?

• y = (x - 6)^2

• y = (x + 6)^2

• y = (x - 3)^2

• y = (x + 3)^2

How do you find the x-intercepts of the equation y = x^2 - 4?

• Set x to 4 and solve for y

• Set x to 0 and solve for y

• Set y to 0 and solve for x

• Set y to 4 and solve for x

What is the factored form of the quadratic equation x^2 - 9x + 18?

• x - 2 and x - 9

• x - 3 and x - 6

• x + 3 and x + 6

• x + 2 and x + 9

What is the GCF of the terms in the equation x^2 - 7x?

• 7x

• x

• 7

• x^2

What is the solution to the equation 3(x - 3)^2 = 27 using the square root method?

• x = 3 and x = -3

• x = 6 and x = 0

• x = 1 and x = -1

• x = 9 and x = -9

What is the first step in solving the equation 16t^2 - 4 = 0 using the square root method?

• Add 4 to both sides

• Divide by 16

• Subtract 4 from both sides

• Take the square root of both sides

What are the solutions to the equation x^2 - 4x + 4 = 0?

• x = 2

• x = 4

• x = -2

• x = -4