Understanding Parabolas

What is the role of the focus in a parabola?

• It is the endpoint of the parabola.

• It is a special point inside the parabola.

• It is a point outside the parabola.

• It is the midpoint of the parabola.

How is the distance 'p' between the vertex and the focus determined?

• By the length of the parabola.

• By the width of the parabola.

• By the coordinates of the vertex.

• By the direction from the vertex to the focus.

What happens to the parabola if 'p' is positive?

• The parabola becomes a straight line.

• The parabola opens to the left.

• The parabola opens upward.

• The parabola opens downward.

What is the directrix in relation to a parabola?

• A vertical line inside the parabola.

• A horizontal line that the parabola never crosses.

• A diagonal line through the vertex.

• A line that intersects the focus.

How does the equation of a parabola change when it opens left or right?

• The equation becomes linear.

• The equation becomes a circle.

• The x and y variables switch places.

• The equation remains the same.

In a parabola that opens left or right, what does a positive 'p' indicate?

• The parabola opens upward.

• The parabola opens downward.

• The parabola opens to the left.

• The parabola opens to the right.

What is the significance of the directrix in a parabola?

• It is the lowest point of the parabola.

• It is the axis of symmetry.

• It is a boundary line that the parabola never crosses.

• It is the highest point of the parabola.

How do you determine the vertex of a parabola given the focus and directrix?

• It is the midpoint between the focus and directrix.

• It is the same as the focus.

• It is the same as the directrix.

• It is the endpoint of the parabola.

What is the relationship between the vertex, focus, and directrix in a parabola?

• The focus is always above the directrix.

• The directrix is always below the vertex.

• The vertex is equidistant from the focus and directrix.

• They are all collinear.

In a parabola, what does the term 'h' and 'k' represent?

• The length of the directrix.

• The width of the parabola.

• The coordinates of the vertex.

• The coordinates of the focus.