Graphing Parabolas in conic sections

The video tutorial explains how to determine the axis of symmetry for parabolas, whether vertical or horizontal. It covers writing parabolas in standard form, identifying parameters like vertex and focus, and calculating these values. The tutorial also discusses how to determine the direction a parabola opens and concludes with finding the directrix. The focus is on understanding the relationships between these elements and applying them to solve problems.

What determines whether a parabola has a vertical or horizontal axis of symmetry?

• The coefficient of the x term

• The presence of an x squared term

• The slope of the line

• The value of the y-intercept

In the standard form of a parabola's equation, what does the variable 'P' represent?

• The slope of the parabola

• The x-coordinate of the vertex

• The y-coordinate of the vertex

• The distance from the vertex to the focus

How do you determine the vertex of a parabola from its equation?

• By setting the equation equal to zero

• By finding the midpoint of the focus and directrix

• By calculating the average of the x and y coefficients

• By taking the opposite of the terms in the equation

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

• The focus is always on the x-axis

• The focus is a fixed distance from the vertex

• The focus is always at the origin

• The focus is always below the vertex

How do you find the directrix of a parabola?

• By subtracting the value of P from the y-coordinate of the vertex

• By adding the value of P to the y-coordinate of the vertex

• By finding the midpoint between the vertex and the focus

• By setting the x-coordinate of the vertex to zero

What happens to the parabola if the focus is above the vertex?

• The parabola opens downwards

• The parabola becomes a circle

• The parabola becomes a line

• The parabola opens upwards

Which of the following is true about the directrix of a parabola?

• It is always perpendicular to the axis of symmetry

• It is always at the origin

• It is always parallel to the y-axis

• It is always parallel to the x-axis