Graphing a Parabola with a vertical shift

The video tutorial explains how to graph the quadratic equation y = X^2 - 4. It begins with an introduction to the parent graph and then discusses the vertex form of a quadratic equation. The instructor demonstrates how to shift the graph down by 4 units, explaining the role of the K value in the vertex form. The lesson concludes with a reconstruction of the graph and a Q&A session to address student queries.

What is the initial step in graphing the equation y = X^2 - 4?

• Calculate the slope

• Understand the parent graph

• Determine the y-intercept

• Identify the vertex of the graph

How does the -4 in the equation y = X^2 - 4 affect the graph?

• It shifts the graph 4 units to the left

• It shifts the graph 4 units to the right

• It shifts the graph 4 units down

• It shifts the graph 4 units up

What is the new vertex of the graph after shifting it down 4 units?

• 4 units below the origin

• At the origin

• 4 units to the right of the origin

• 4 units above the origin

In the vertex form y = a * (X - H)^2 + K, what role does K play?

• It shifts the graph vertically

• It affects the width of the graph

• It changes the direction of the graph

• It determines the horizontal shift

If K is positive in the vertex form, how does it affect the graph?

• The graph shifts K units down

• The graph shifts K units up

• The graph shifts K units to the left

• The graph shifts K units to the right