Understanding Parabolas: Focus and Directrix

The video explores an alternate method to find the focus and directrix of a parabola from its equation. It begins by solving the equation for y, then reviews the concepts of focus and directrix. The video explains how to identify the vertex and determine the parabola's orientation. It includes a hand-drawn graph to visualize the parabola and concludes with calculating the focus and directrix using the vertex.

What is the primary goal of the video regarding the parabola?

• To graph the parabola accurately

• To explore an alternate method for finding the focus and directrix

• To find the vertex of the parabola

• To solve for x in the parabola equation

In the context of a parabola, what does the term 'directrix' refer to?

• A line y equals k

• The maximum point of the parabola

• A line parallel to the x-axis

• A point on the parabola

How is the vertex of a downward opening parabola described?

• As the maximum point

• As the intersection point

• As the minimum point

• As the midpoint

What does the negative coefficient in front of the squared term indicate about the parabola?

• It has no vertex

• It is a linear equation

• It opens downwards

• It opens upwards

Where does the focus of a parabola lie in relation to its vertex?

• On the same y-coordinate

• On the same x-coordinate

• At the origin

• At the midpoint of the parabola

What is the relationship between the vertex and the focus and directrix?

• The vertex is unrelated to the focus and directrix

• The vertex is closer to the directrix

• The vertex is equidistant from the focus and directrix

• The vertex is closer to the focus

How is the distance between the focus and directrix determined?

• By the absolute value of b minus k

• By the x-coordinate of the vertex

• By the y-coordinate of the vertex

• By the slope of the parabola

What is the calculated y-coordinate of the directrix in this example?

• 7

• 6.5

• 6

• 5

What is the x-coordinate of the focus in this example?

• 0

• 1

• 2

• 3

What is the y-coordinate of the focus in this example?

• 7

• 4

• 5

• 6