Finding the vertex and zeros of a quadratic function

The video tutorial covers the process of finding the vertex and intercepts of a quadratic function. It begins with an introduction to the problem and the quadratic form, followed by a detailed explanation of completing the square to find the vertex. The tutorial then demonstrates converting the function to vertex form and calculating the vertex. Finally, it explains how to find the X intercepts using the quadratic formula.

What is the first step in setting up a quadratic function to find its vertex?

• Find the x-intercepts

• Convert it to standard form

• Use the quadratic formula

• Graph the function

What mathematical method is used to transform a quadratic function into vertex form?

• Graphing

• Using the quadratic formula

• Completing the square

• Factoring

When completing the square, what must be done to maintain the balance of the equation?

• Add a constant to both sides

• Subtract the same value added inside the parentheses

• Multiply the entire equation by a constant

• Divide the equation by the leading coefficient

What is the vertex of the quadratic function after completing the square?

• (2, -5)

• (5, -2)

• (-2, 5)

• (-5, 2)

What is the purpose of using the quadratic formula in this context?

• To find the vertex

• To determine the y-intercept

• To find the x-intercepts

• To convert to standard form

Which of the following is a step in finding the x-intercepts using the quadratic formula?

• Setting the quadratic equation equal to zero

• Completing the square

• Graphing the function

• Finding the derivative of the function

What are the x-intercepts of the function after applying the quadratic formula?

• (-2 + sqrt(5), 0) and (-2 - sqrt(5), 0)

• (5 + sqrt(2), 0) and (5 - sqrt(2), 0)

• (-5 + sqrt(2), 0) and (-5 - sqrt(2), 0)

• (2 + sqrt(5), 0) and (2 - sqrt(5), 0)