Learning to graph a parabola and determine the vertex focus and directrix

The video tutorial explains the standard form of conic sections, focusing on the equation y - K^2 = 4P(x - H). It covers how to determine the vertex, focus, and directrix of the conic section, and how to plot these on a graph. The tutorial emphasizes understanding the direction in which the graph opens, based on whether the equation involves y^2 or x^2. The instructor provides step-by-step guidance and clarifies common misconceptions, ensuring students can accurately plot and interpret conic sections.

What is the standard form of the equation for a conic section that opens horizontally?

• x - K^2 = 4P(y - H)

• x - H^2 = 4P(y - K)

• y - K^2 = 4P(x - H)

• y - H^2 = 4P(x - K)

How do you determine the vertex of a conic section?

• By solving the equation for x and y

• By finding the midpoint of the focus and directrix

• By using the coordinates (H, K)

• By calculating the average of x and y intercepts

What is the role of the value 'P' in the equation of a conic section?

• It indicates the direction of the opening

• It determines the width of the parabola

• It is the slope of the directrix

• It is the distance from the vertex to the focus

In which direction does a conic section open if the equation is y - K^2 = 4P(x - H) and P is positive?

• Upwards

• To the right

• To the left

• Downwards

What is the equation of the directrix if the focus is at (3, 1) and P is 2?

• x = -7

• x = -1

• x = 1

• x = 5