Writing Quadratic Functions in Vertex Form

Mr. Allen provides a tutorial on converting quadratic functions from standard form to vertex form by completing the square. He demonstrates the process with two examples, explaining each step in detail. The video emphasizes the importance of completing the square in mathematics and provides tips for simplifying the process. The tutorial concludes with a brief discussion on finding the vertex from the vertex form.

What is the first step in transforming a quadratic function to vertex form?

• Divide both sides by a constant

• Multiply both sides by a constant

• Subtract a constant from both sides

• Add a constant to both sides

In the first example, what number is added to both sides after dividing -14 by 2 and squaring it?

• 7

• 14

• 49

• 28

What is the vertex of the quadratic function after completing the square in the first example?

• (7, -46)

• (7, 46)

• (-7, 46)

• (-7, -46)

What is the final form of the quadratic function in the first example after completing the square?

• f(x) = (x + 7)^2 - 46

• f(x) = (x + 7)^2 + 46

• f(x) = (x - 7)^2 + 46

• f(x) = (x - 7)^2 - 46

Why is the number obtained by dividing the coefficient of x by 2 and squaring it important?

• It simplifies the equation

• It changes the function to standard form

• It helps in factoring the quadratic expression

• It eliminates the x term

In the second example, what number is added to both sides after dividing 2 by 2 and squaring it?

• 0

• 1

• 2

• 4

What is the vertex of the quadratic function after completing the square in the second example?

• (-1, -11)

• (-1, 11)

• (1, -11)

• (1, 11)

What is the final form of the quadratic function in the second example after completing the square?

• G(x) = (x + 1)^2 - 11

• G(x) = (x + 1)^2 + 11

• G(x) = (x - 1)^2 + 11

• G(x) = (x - 1)^2 - 11

What is the purpose of completing the square in transforming quadratic functions?

• To eliminate the x term

• To simplify the function

• To convert the function to vertex form

• To find the roots of the function

What should you do if you want to practice more problems on completing the square?

• Read a textbook

• Practice with different quadratic functions

• Watch more videos

• Ask a teacher for help