How to sketch a parabola by finding the focus and directrix

The video tutorial explains how to determine the orientation of a parabola by examining what is squared in the equation. It covers rewriting the equation in standard form, identifying the vertex, and isolating X squared. The tutorial also demonstrates how to find the focus and directrix of the parabola and concludes with graphing the parabola, showing the relationship between the vertex, focus, and directrix.

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

• By examining what is being squared

• By checking the constant term

• By analyzing the linear term

• By looking at the coefficient of Y

What is the purpose of rewriting a parabola equation in standard form?

• To simplify the equation for graphing

• To find the roots of the equation

• To calculate the area under the curve

• To determine the axis of symmetry

What is the value of P if the equation is X^2 = 2Y?

• 1/2

• 2

• 1

• 4

How is the focus of a parabola related to its vertex?

• The focus is always below the vertex

• The focus is at the same point as the vertex

• The focus is a fixed distance P from the vertex

• The focus is always above the vertex

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

• The focus is always to the left of the directrix

• The directrix is always above the focus

• They are equidistant from any point on the parabola

• They are at the same point

In which direction does a parabola open if the focus is at (0, 1/2)?

• Upwards

• Right

• Downwards

• Left

Where is the directrix located if the focus is at (0, 1/2)?

• y = 1/2

• y = -1/2

• x = -1/2

• x = 1/2