Completing the Square and Vertex Form

The video tutorial explains how to convert a quadratic function into vertex form. It begins by grouping the x terms and factoring out a common factor. The process of completing the square is demonstrated, including the necessary adjustments to maintain equality. Finally, the vertex form is derived, and the characteristics of the parabola, such as its vertex and direction, are discussed.

What is the vertex form of a quadratic function?

• F(x) = a(x - h)^2 + k

• F(x) = ax^2 + bx + c

• F(x) = a(x + h)^2 - k

• F(x) = ax + b

What is the first step in completing the square for the quadratic function?

• Add the square of the constant term

• Factor out the common factor from the x terms

• Multiply the entire equation by 2

• Subtract the constant term from both sides

When completing the square, what do you add inside the parentheses?

• The square of the entire expression

• The square of the constant term

• The square of half the coefficient of x

• The square of the coefficient of x

After completing the square, what adjustment is made outside the parentheses to maintain equality?

• Add the same value that was added inside

• Subtract the product of the factor and the added value

• Multiply the entire equation by the factor

• Divide the entire equation by the factor

What is the vertex of the parabola given by the function f(x) = 2(x + 3)^2 + 4?

• (3, 4)

• (-3, 4)

• (3, -4)

• (-3, -4)