Vertex Form and Quadratic Methods

This video tutorial teaches how to convert a quadratic equation from standard form to vertex form using two methods: the negative B over 2A formula and completing the square. The instructor provides step-by-step examples for each method, highlighting key calculations and concepts. The video also includes practice problems to reinforce learning and offers insights into the effects of transformations on the graph of a quadratic function.

What are the two methods discussed for converting a quadratic equation from standard form to vertex form?

• Factoring and using synthetic division

• Finding the vertex and completing the square

• Using the quadratic formula and factoring

• Graphing and using the quadratic formula

Which formula is used to find the x-coordinate of the vertex in the first method?

• C - A

• A + B + C

• 2A/B

• -B/2A

In the first example, what is the x-coordinate of the vertex when using the -B/2A method?

• 2

• -2

• 4

• 0

What is the purpose of completing the square in the second method?

• To factor the equation

• To simplify the equation

• To convert the equation to vertex form

• To find the roots of the equation

What is the first step in completing the square for the first example?

• Add 1 to both sides

• Subtract 1 from both sides

• Multiply by 2

• Divide by 3

What is the result of completing the square in the first example?

• y = 3(x + 2)^2 - 13

• y = 3(x - 2)^2 - 13

• y = -3(x + 2)^2 + 13

• y = -3(x - 2)^2 + 13

What is the x-coordinate of the vertex in the second example using the -B/2A method?

• -2

• 2

• -4

• 4

In the second example, what is the y-coordinate of the vertex after using the -B/2A method?

• 0

• 5

• -3

• 3

What is the first step in completing the square for the second example?

• Multiply by 2

• Subtract 5 from both sides

• Divide by 3

• Add 5 to both sides

What is the final vertex form of the equation in the second example using completing the square?

• y = 1/2(x - 4)^2 - 3

• y = 1/2(x + 4)^2 + 3

• y = 1/2(x - 4)^2 + 3

• y = 1/2(x + 4)^2 - 3