Determine the equation of parabola given the vertex and focus

The video tutorial covers graphing techniques, focusing on plotting vertices and foci, determining the direction of parabolas, calculating the directrix, and writing the standard equation of a graph. The teacher explains the relationship between the vertex, focus, and directrix, and how these elements influence the graph's shape and direction.

What is the role of the focus in determining the direction a parabola opens?

• The focus is irrelevant to the direction.

• The focus determines if the parabola opens left or right.

• The focus must be inside the parabola, determining if it opens up or down.

• The focus only affects the width of the parabola.

How is the directrix related to the focus in a parabola?

• The directrix is always parallel to the focus.

• The distance from the focus to the directrix is equal to the distance from the vertex to the focus.

• The directrix is perpendicular to the axis of symmetry.

• The directrix is irrelevant to the parabola's equation.

What is the standard form of a vertical parabola's equation?

• X = 4PY^2

• Y = 4PX^2

• X^2 = 4PY

• Y^2 = 4PX

If the vertex of a parabola is at the origin and the focus is at (0, -2), what is the value of P?

• 0

• 2

• 4

• -2

What is the final equation of the parabola with a vertex at (0,0) and a focus at (0,-2)?

• X^2 = 8Y

• Y^2 = -8X

• X^2 = -8Y

• Y^2 = 8X