Writing the equation of a parabola given focus and directrix

The video tutorial emphasizes the importance of plotting in solving math problems, particularly focusing on the relationship between the focus, directrix, and vertex of a parabola. It explains how to graph parabolas, determine their orientation, and use the vertex form to simplify equations. The tutorial concludes by highlighting the significance of understanding these concepts to avoid common mistakes.

Why is it important to plot the focus and directrix correctly when working with parabolas?

• To avoid making calculation errors

• To find the axis of symmetry

• To ensure the parabola is symmetrical

• To make the graph look neat

What is the position of the vertex in relation to the focus and directrix?

• It is equidistant from both

• It is closer to the directrix

• It is not related to them

• It is closer to the focus

How does the axis of symmetry relate to the focus and vertex of a parabola?

• It passes through the directrix

• It is perpendicular to the directrix

• It passes through both the focus and vertex

• It is parallel to the directrix

In which direction does a parabola open if its focus is to the left of the vertex?

• To the right

• Downwards

• Upwards

• To the left

What is the formula used to describe a parabola with a horizontal opening?

• y = mx + b

• x = ay^2 + by + c

• x^2 = 4py

• y^2 = 4px