Unit 2 Parabola

Open Ended

Can you think of other real-life objects or structures that use the shape of a parabola for a specific purpose? Explain your answer.

Multiple Choice

Which of the following statements best describes how a parabola is generated from a double-napped cone?

• When a plane is parallel to one generator and intersects only one nappe.

• When a plane is perpendicular to the axis of the cone.

• When a plane intersects both nappes of the cone.

• When a plane is parallel to the base of the cone.

Fill in the Blank

The fixed point not on the directrix of a parabola is called the ___

Multiple Choice

The latus rectum of a parabola is a line segment that:

• Passes through the focus and is parallel to the directrix

• Passes through the vertex and is perpendicular to the axis of symmetry

• Joins the focus and the directrix

• Is tangent to the parabola at the vertex

Multiple Select

Select all the correct statements about a parabola from the options below:

• A parabola is a conic section.

• A parabola is generated when a plane is parallel to one generator of a cone.

• A parabola is the set of all points equidistant from a directrix and a focus.

• A parabola is always a circle.

Multiple Select

Which of the following are parts or properties of a parabola?

• Vertex

• Focus

• Directrix

• Latus rectum

Fill in the Blank

A parabola is the set of all points in a plane that are equidistant from a fixed line called the ___ and a fixed point called the focus.

Multiple Choice

What is the midpoint between the focus and the directrix of a parabola called?

• Vertex

• Axis of symmetry

• Latus rectum

• Focus

Multiple Choice

Which of the following is the standard form of a parabola with its vertex at (0,0) and axis of symmetry along the y-axis?

• x^2 = 4cy

• y^2 = 4cx

• x^2 = 4c(y-k)

• (x-h)^2 = 4c(y-k)

Open Ended

How do you represent a parabola using an equation?

Multiple Choice

Given the equation (y + 3)^2 = 12(x + 1), what are the coordinates of the vertex of the parabola?

• (-1, -3)

• (1, 3)

• (3, 1)

• (-3, -1)

Open Ended

Explain how the standard form of the equation of a parabola changes when the vertex is moved from the origin to a point (h, k).

Multiple Choice

If the equation of a parabola is y^2 = 4cx and c < 0, in which direction does the parabola open?

• Left

• Right

• Upward

• Downward

Fill in the Blank

The standard form of a parabola with vertex (h, k), vertical axis of symmetry, and focus at (h, k + c) is ___

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Fill in the Blank

Determine the equation of the parabola in standard form given its focus at (0, -7) and directrix y = 7.

^

=

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Multiple Choice

Which of the following best describes the axis of symmetry for the parabola with focus at (10, 0) and directrix x = -10?

• vertical

• horizontal

• diagonal

• none

Multiple Select

Select all that are true for the parabola given by (y - 6)^2 = 12(x + 5).

• The vertex is at (-5, 6)

• The focus is at (-2, 6)

• The directrix is x = -8

• The axis of symmetry is vertical

Open Ended

Find the vertex, focus, and directrix of the parabola given by the equation (x - 3)^2 = 8(y + 5).

Open Ended

Find the standard form of the equation of the parabola given that the vertex is at (2, 1) and the focus at (2, 4).

Fill in the Blank

Fill in the blank: The standard form of the equation of the parabola with vertex at (2, 1) and focus at (2, 4) is (x - 2)^2 = ___(y - 1).

Multiple Choice

Which of the following is the correct standard form of the equation of the parabola with vertex at (5, -2) and focus at (7, -2)?

• (y + 2)^2 = 8(x - 5)

• (x - 5)^2 = 8(y + 2)

• (x - 5)^2 = 8(y - 2)

• (y - 2)^2 = 8(x - 5)

Open Ended

What is one real-world application of a parabola that you learned about in this lesson?

Open Ended

How does the parabolic shape of a satellite dish help it receive signals effectively?

Open Ended

What is one real-world application of a parabola that you learned about today, and how does it relate to the topic of parabolas?

Open Ended

How does the parabolic shape of a satellite dish help it receive signals effectively?