Given the focus and vertex write the equation of a parabola

The video tutorial explains how to approach problems involving parabolas, focusing on graphing given information such as the focus, vertex, and directrix. It emphasizes the importance of plotting and labeling these elements. The tutorial covers the orientation of parabolas and the relationship between the directrix, vertex, and focus. It concludes with deriving the equation of a parabola using the distance from the vertex to the focus.

Why is it important to graph and label the focus, vertex, and directrix when solving parabola problems?

• It is necessary for determining the color of the parabola.

• It is required for calculating the area of the parabola.

• It helps in finding the length of the parabola.

• It helps in visualizing the problem and understanding the parabola's orientation.

What is the relationship between the vertex, focus, and directrix of a parabola?

• The vertex is not related to the focus and directrix.

• The vertex is closer to the focus than to the directrix.

• The vertex is twice the distance from the focus as it is from the directrix.

• The vertex is equidistant from the focus and the directrix.

How do you determine the direction in which a parabola opens?

• By the color of the graph.

• By the position of the directrix.

• By the position of the focus relative to the vertex.

• By the length of the parabola.

In the context of parabolas, what does the variable 'P' represent?

• The distance from the focus to the directrix.

• The distance from the vertex to the origin.

• The distance from the vertex to the focus.

• The distance from the vertex to the directrix.

What is the final equation of the parabola derived in the tutorial?

• y^2 = 8x

• y^2 = 4x

• x^2 = 4y

• x^2 = 8y