How to complete the square to identify the vertex of a parabola

The video tutorial covers writing quadratic equations in standard and vertex forms, emphasizing the importance of the vertex form for easy identification of the vertex. It explains the process of completing the square to convert a quadratic equation into vertex form, including factoring and finding the value that completes the square. The tutorial also discusses solving equations and the concept of equivalent equations, using examples to illustrate these ideas. Finally, it demonstrates how to find the vertex of a quadratic equation using the completed square method.

What is the primary reason for writing a quadratic equation in the form y = a(x-h)^2 + k?

• To find the roots of the equation

• To make the equation easier to solve

• To easily identify the vertex

• To simplify the equation

What is the first step in completing the square for a quadratic equation?

• Factor out the coefficient of x^2

• Group the first and last terms

• Add and subtract the same number

• Solve for x

If the coefficient of x^2 is not 1, what should you do before completing the square?

• Add 1 to the equation

• Factor out the coefficient

• Multiply the equation by 2

• Subtract the coefficient

How do you find the value that completes the square in a quadratic equation?

• Subtract the constant term from the coefficient of x

• Multiply the coefficient of x by 2 and square it

• Add the coefficient of x to the constant term

• Divide the coefficient of x by 2 and square it

What is the result of adding and subtracting the same number inside and outside the parentheses in completing the square?

• It changes the equation

• It solves the equation

• It simplifies the equation

• It keeps the equation equivalent

After completing the square, what is the vertex of the equation y = (x + 8)^2?

• (-8, 0)

• (8, 0)

• (0, 8)

• (0, -8)

Why is it important to perform the same operation on both sides of an equation?

• To solve the equation

• To change the equation

• To maintain equality

• To simplify the equation