Learn how to find the equation of a parabola given focus and vertex conic sections

The video tutorial explains how to analyze a parabola by identifying its vertex and focus, understanding the graph's structure, calculating the directrix and axis of symmetry, and deriving the equation of the parabola. The teacher guides students through the process of visualizing and writing the equation, emphasizing the relationship between the vertex, focus, and directrix.

What are the coordinates of the vertex given in the problem?

• (2, 0)

• (0, 2)

• (0, 0)

• (2, 2)

How do you determine the position of the directrix?

• By drawing a line parallel to the axis of symmetry

• By using the formula y = mx + c

• By finding the midpoint between the vertex and the focus

• By moving the same distance from the vertex as the focus but in the opposite direction

What is the equation of the axis of symmetry for this parabola?

• x = 2

• y = 0

• x = 0

• y = 2

In which direction does the parabola open?

• To the right

• To the left

• Downwards

• Upwards

What is the equation of the parabola derived in the video?

• x^2 = 8y

• y^2 = 8x

• y^2 = 4x

• x^2 = 4y